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r <? 







THE STEAM ENGINE 
AND TTTEBINE 



A TEXT-BOOK 
FOR ENGINEERING COLLEGES 



BY 



ROBERT C. H. HECK, M.E. 

Professor of Mechanical Engineering, Rutgers College 



ILLUSTRATED 




NEW YORK 

D. VAN NOSTRAND COMPANY 

23 Murray and 27 Warren Streets 
1911 






Copyright, 1911, 

BY 

D. VAN NOSTRAND COMPANY 



\ 



«i 








Stanbope iPtess 

F. H. GILSON COMPANY 
BOSTON. U.S.A. 



CCLA3051H8 



PREFACE 



In part this book is adapted from the writer's Steam Engine and 
Other Steam Motors, in larger part it is rewritten or newly written. 
The textbook idea and the purpose of class-room use have continually 
been kept in mind. Mechanical form and manner of working are illus- 
trated by selected, typical examples of construction; rational theory 
is built up, from fundamental concepts to the fully-developed ideal 
steam engine; and actual performance is studied and compared with 
the ideal, an especial effort being made to set forth clearly and logically 
the empirical knowledge which must fill the gap between them. 

Viewing the steam plant as a whole, a line is drawn between the 
members that have to do with the generation and impartation of heat, 
and those concerned with its conversion into work through the agency 
of steam. In other words, the furnace and boiler, with their acces- 
sories, are taken to constitute a subject for treatment elsewhere, except 
that allusion is freely made to their functions. But on the side of the 
steam machine a comprehensive presentation is undertaken: to the 
writer it appears that the study of the piston engine and of the turbine 
can most effectively and profitably be combined in a single course. 

It is assumed that the student approaches the subject with at least 
a general knowledge of the form and working of the steam plant, and 
with a good preparation in the elements of physics and of mechanics. 
All deductions along the latter lines begin, however, with basal facts or 
principles, so that the book shall be self-contained on that side. In 
the matter of thermodynamics, which is carried only so far as it is of 
immediate use and application, a special effort is made to develop con- 
cepts and ideas, not merely to build up a mathematical, abstract struc- 
ture on a few axioms. An excess of mathematics is avoided, preference 
being largely given to graphical methods. Many numerical examples 
illustrate and enforce the text, emphasize the quantitative side of the 
subject, and will suggest problems for class-room use. 

Certain omissions imply supplementation by other parts of the cur- 
riculum. Directions for making tests are left to the laboratory course, 
although the purpose of such tests, the quantities sought, and the 

iii 



iv THE STEAM ENGINE AND TURBINE 

manner of workup are fully indicated. Design goes no farther than 
proportioning of the parts that have to do with steam action, not ex- 
tending into the field of machine design. Plant layout and economics, 
to a generally sufficient extent, can be covered by a few lectures, with 
visits of inspection. Engine or plant manipulation is hardly a matter to 
be learned from books. 

A new steam table is presented, differing slightly from that of Marks 
and Davis, but founded on the same experimental data. For saturated 
steam, it was worked out before the latter appeared; in continuity and 
smoothness it is a little better, especially in the high range of pressure; 
while for superheated steam, the line of equal temperature, used in 
Table VII and described on page 86, is a new and most effective means 
of correlating data as to total heat. 

As between engine and turbine, the former receives much the larger 
share of space, although the difference is less than may appear, since 
Chapters I to IV and the first part of Chapter VI apply to both. Of in- 
tention, however, the engine is given fuller treatment: the problems of 
its intimate behavior have been more fully worked out or solved by 
experience, so that they come within textbook scope; and a general text 
like this may aim to be fairly complete, within its field, for the engine, 
while very properly making frequent reference to large and special 
works on a growing subject, such as Stodola's Steam Turbines. 

The arrangement of the book is intended to facilitate selection and 
omission, with §§ 22 to 25 most strongly indicated for briefer summariza- 
tion in lecture. The section on condensers brings that rapidly-develop- 
ing subject up to date, in good shape for the student. 



CONTENTS 



CHAPTER I 
A General View of the Subject 

Pagh 
§ 1. The Steam-power Plant 1 

Outline of simple plant, form and functions of members. 

§ 2. Construction and Working of the Engine 5 

High-speed and Corliss types; main mechanism and its parts; indicator diagram, 
steam and valve action, governing. 

§ 3. Classification and Characteristics of Engines 20 

Classification by service and form, layout, speed range . 

§ 4. The Steam Turbine 22 

General description of steam action, typical example of each class. 

CHAPTER II 
Elementary Theory of the Heat Engine 
§ 5. Heat and Work 33 

General definitions and relations. 

§ 6. The Perfect Gas 35 

General law of relation, law of Gay Lussac, absolute temperature, coefficient of 
expansion, Mariotte's law. 

§ 7. Simple Thermodynamic Operations with Gases 41 

Effects of heat, constant pressure and constant volume, specific heat, isothermal 
expansion, law pv n = constant, adiabatic expansion and curve. 

§ 8. The Ideal Heat Engine 49 

General ideas, Carnot cycle, various efficiencies, availability of this cycle. 

§ 9. The Temperature-entropy Analysis 55 

Idea of entropy, simple examples. 

§ 10. General Principles of the Heat Engine 58 

Availability of energy, efficiency in conversion, hydraulic analogy, reversibility of 
process and of cycle, argument from reversibility. 

CHAPTER III 

Properties and Behavior of Steam 
§ 11. Generation and Properties of Steam 66 

Operation of making steam, quantitative data, steam tables. 

§ 12. The Pressure and Volume of Steam 67 

Pressure-temperature relation; specific volume and density, the pv product, satura- 
tion line; volume of superheated steam, constant-pressure expansion, volume and 
temperature, isothermal curve. 

V 



VI THE STEAM ENGINE AND TURBINE 

Page 
§ 13. Thermal Properties of Steam 79 

Specific heat of water, heat of liquid and of vaporization, total heat, heat of forma- 
tion; external work and internal energy; superheated steam, specific heat, total heat, 
internal energy, specific heat at constant volume; entropy of steam and entropy 
diagram. 

§ 14. Various Curves and Operations 91 

Adiabatic expansion and its characteristics, form of adiabatic curve; curve of con- 
stant steam weight; equilateral hyperbola. 



CHAPTER IV 

Ideal Steam Cycles 
§ 15. The Static Pressure Cycle 100 

Carnot cycle with steam and its availability; separation of function and the Rankine 
cycle; ideal steam diagram, incomplete expansion, thermal diagram, work per pound 
of steam. 

§ 16. The Dynamic Force Cycle Ill 

The steam jet, formation, energy, and form; steam-jet tables; similarity of jets, 
comparison of areas; the Napier divisor; effect of initial condition, flow of steam and 
of hot water. 

§ 17. Throttling or Kinetic Pressure Lowering 128 

Action of throttling; lines of constant total heat, continuous throttling, increase of 
entropy, energy transformed; reversibility of steam-jet cycle; fall of temperature in 
throttling; the throttling calorimeter, use and range; separator calorimeter, accuracy 
of steam calorimetry. 

§ 18. Special Graphical Methods 138 

Mollier diagram, layout and meaning; other schemes. 



CHAPTER V 
Action of the Steam in the Engine 
§ 19. The Indicator Diagram v 142 

Detailed comparison of indicator diagram and ideal steam diagram, with discussion 
of kinetic losses and preliminary consideration of clearance and compression. 

§ 20. The Compound Engine 150 

Objects of compounding, general scheme and simple diagram; arrangement and 
working, typical lines of intermediate pressure; indicator diagrams and their 
combination. 

§ 21. Horse Power and Steam Consumption 159 

Meaneffective pressure, work per revolution, indicated horse-power, cylinder con- 
stants; indicated steam consumption, simple and compound diagrams; measurement 
of actual steam, curves and diagrams of consumption, various steam quantities, the 
unit diagram. 

§ 22. Effect of the Cylinder Walls 175 

Formula for missing steam; diagrams of various engine tests, showing effect of varia-' 
tion in cut-off, of throttling, of speed, of temperature and pressure range; engines 
with large compression; influence of size; leakage. 

§ 23. Effects of Compression 199 

Fuller analysis of compression, with test results and conclusions. 

§ 24. Analysis for Thermal Effect 209 

Determination of heat interchanges, Hirn's analysis and cognate ideas; temperature- 
entropy diagram for the engine. 

§ 25. Thermal Action of the Cylinder Walls 218 

Experimental work on wall action; steam temperature cycle; Callendar and Nicholson 
experiments, method, results, and deductions; Duchesne experiments. 






CONTENTS. vii 

CHAPTER VI 

Performance and Efficiency of the Engine 

Page 
26. Measures of Performance 231 

Steam consumption, thermodynamic efficiencies, heat in feed water, plant efficiencies 
working of auxiliaries; heat consumption; duty; relative efficiency discussed, eco- 
nomical vacuum; equivalent steam rates. 

§ 27. Examples of Performance 244 

Steam diagrams on unit basis; large compression, small compression, jackets and 
reheaters, superheated steam, regenerative cycle; table of selected test results; dia- 
grams of plant performance. 

§ 28. Friction and Machine Efficiency ■. 275 

Types of loading, friction load and power, examples of performance, frictional 
m.e.p., friction by force analysis. 

§ 29. Proportioning Engine Cylinders 281 

Ideal diagram and diagram factor, examples from engines; determining size and 
speed; proportioning cylinders of compound engines, methods and relations. 

CHAPTER VII 

Working and Construction of the Engine 

§ 30. Forces in the Machine 291 

General view of all the forces in the engine. 

§ 31. Motion of the Engine Mechanism 298 

Kinematic analysis, leading to velocity and acceleration diagrams for the piston. 

§ 32. Working Forces in the Engine 308 

Inertia force, effective steam pressure, driving force, turning force and its diagrams, 
fly-wheel data. 

§ 33. Fly-wheel Action 321 

Weight of wheel; effective radius; multiple-crank arrangements; stress in rim of 
wheel, limiting speed. 

§ 34. Pressures on Pins and Bearings 327 

Pressure diagrams, reversal of force, guide-bar pressures, bearing pressures. 

§ 35. .Balancing the Engine 334 

Shaking force and counterbalance, force diagrams; the duplex engine; shifting and 
torque effects; rod effect; method of radial resultants. 

§ 36. Construction of the Engine 343 

Selected examples, construction of cylinder, frame, piston and crosshead, connecting 
rod, shaft and bearings, wheels. 

CHAPTER VIII 

Valve Gears and Governors 

§ 37. The Simple Slide Valve, with Harmonic Motion 362 

Reuleaux and Zeuner diagrams, complete valve diagram, valve and piston diagram, 
characteristics of valves, effect of rocker arm. 

§ 38. Various Valve-gear Relations 371 

Bilgram diagram; geometrical relations, problems; valve setting; secondary disturb- 
ing actions. 

§ 39. The Shifting Eccentric: Variable Steam Distribution 376 

Moving the eccentric center; shaft-governor action, diagrams and problems; width 
of port opening, symmetrical admission, indicator diagrams, influence of lead. 

§ 40. Reversing Valve Gears 382 

Stephenson gear, form, arrangement, diagrams; radial gears, Walschaert and Joy. 

§ 41. The Double-valve Gear 391 

Meyer gear; relative valve movement, function of cut-off valve, positive and negative 
valves; eccentric setting, varying cut-off, indicator diagrams. 



viii THE STEAM ENGINE AND TURBINE. 

Page 
§ 42. Details of Slide Valves and Gears 396 

Characteristics of valves; examples of slide valves; multiple admission and balancing; 
design of steam passages, proportioning valves; valve-gear parts. 

§ 43. The Corliss Valve Gear 403 

Full description of a simple gear and its working; valve motion curves, eccentric 
setting; valve resistance; various forms of valve; use of two eccentrics; the dashpot. 

§ 44. Various Valve Gears 417 

Gridiron valve gears; non-harmonic gears with variable eccentric; lift-valve engines, 
types of valve, arrangement and details of gear; engine without crank shaft, steam 
actuated valves; self-centering valve. 

§ 45. Steam-engine Governors : 426 

Functions, typical force action, stability, adjustment; regulation by fly-ball gov- 
ernor; force action in the shaft governor, types of this device; control of regulation; 
throttling governor. 

CHAPTER IX 

Action of the Steam in the Turbine 
§ 46. Dynamics of Jet Action 434 

Impulse, reaction, and deflection of jet; driving force on vanes; work on vanes; speed 
relations; channel form and section; multiple-impulse action; path and absolute ve- 
locity of jet. 

§ 47. Experiments on the Steam Jet 452 

Flow through orifices and nozzles, various experiments; detailed observations on jet, 
pressure, temperature, efficiency; calculation of efficiency; flow in curved channels, 
impulse upon vanes, impulse of jet from vanes; energy losses in turbine. 

§ 48. Turbine Performance 477 

Table of selected test results; influence of size, load, steam condition, pressure range, 
superheat, vacuum, and speed; performance by stages, the Mollier diagram; com- 
bined engine and turbine unit; estimate of losses. 

CHAPTER X 

Design and Construction of the Turbine 
§ 49. Design for Steam Action 503 

Dimensions of steam channel; multistage turbine, use of Mollier diagram; propor- 
tions of stages and of vane channels. 

§ 50. Various Forms of the Turbine 510 

Types of steam action, directions of flow; variations of impulse and of reaction tur- 
bines; low-pressure and mixed-flow turbine; Rateau accumulator; marine turbine, 
geared turbine. 

§ 51. Construction of Working Parts 516 

Rotors, disc wheels, drum rotors, centrifugal stress and balance; bearings, stuffing 
boxes; nozzles or distributors, vanes or blades, wear on vanes; governing the turbine, 
puff governing, cut-off control, effects of governer action. 

CHAPTER XI 

Sundry Steam Appliances 
§ 52. Steam Jet Apparatus 537 

Entrainment by jet; steam blowers; the injector, types, theory of action, test of 
performance, range of working. 

§ 53. Condensers and Air Pumps 545 

Principle of condensation, types of condensers, removal of condensate, the gas and 
vapor mixture; quantity of air to be handled; countercurrent condensers; action and 
efficiency of cooling surface, performance of surface condensers; various surface con- 
densers; air pumps, clearance and volumetric efficiency, water ejectors, power for 
condenser pumps; the cooling tower, the self-cooling condenser. 

§ 54. The Rotary Engine 570 

General idea and simple example* 



CONTENTS. ix 



APPENDIX 



TABLES OF THE PROPERTIES OF STEAM 

Page 

§ A. List of Tables and Diagrams 573 

§ B. Alphabetical List of Symbols 574 

§ C. Accuracy of the Steam Table 577 

§ D. Notes on Steam-table Data 616 

Table I. Temperatures for Various Pressures 578 

Table II. Principal Steam Table 580 

Table III. Supplementary Steam Table 602 

Table IV, V. Factors for Volume Calculation 603 

Table VI. Volume of Superheated Steam 604 

Table VII. Total Heat of Superheated Steam 606 

Table VIII. Entropy of Superheated Steam 611 

Index 619 



REFERENCE TABLES IN TEXT 

Number Subject Page 

1, 2 Speed of Engines 21 

3 Factors for Adiabatio Curve of Air 47 

4 Pressure Unit Ratios 69 

5 Comparison of Adiabatic Curves of Steam 95 

6, 7 Steam Jet Tables 116-118 

8 Napier Divisor, Initial Quality Variant 125 

9 Cylinder Constants 162 

10 Temperature Function for Condensation Formula 179 

Power Unit Ratios .-." 231 

11 Thermal Efficiency and Heat Supply 239 

12 Rankine Cycle Outputs 242 

13 Tests of Various Steam Engines 268-271 

14 Examples of the Diagram Factor 285 

15 • Turning Force Ratios 316 

16 Sample Fly-wheel Data 320 

17 Peabody Steam-jet Experiments 452 

18 Rateau's Experiments on Flow of Steam 454 

19 Efficiency Results, Steam Nozzle Tests 468 

" 20 Tests of .Various Steam Turbines 478-485 

21 Efficiency, Various Types of Turbines 487 

22 Turbine Tests Showing Effect of Superheating 492 

23 Tests Showing Variation of Vacuum 493 

24 Test of Turbine by Stages 498 

25 Results from Engine and Turbine Unit 500 

26 Performance of Surface Condensers .* 560 



THE STEAM ENGINE AND TURBINE. 



EQUATIONS AND FORMULAS IN TEXT 



Number 


Page 


Number 


Page 


Number 


Page 


Number 


Page 


1-3 


35 


88 


91 


136-138 


232 


203 


341 


4-7 


36 


89-93 


92 


139 


240 


204 


369 


8-11 


39 


94 


95 


140 


264. 


205 


386 


12 


40 


95 


96 


141 


279 


206 


390 


13 


41 


96-97 


101 


142 


284 


207 


400 


14-17 


42 


98-100 


105 


143 


286 


208-210 


426 


18-21 


43 


101 


109 


144-145 


287 


211-212 


434 


22-23 


44 


102 


110 


146-149 


288 


213-216 


435 


24-29 


45 


103-104 


112 


150 


293 


217-218 


438 


30-35 


46 


105 


113 


151-152 


299 


219-221 


440 


36 


51 


106-107 


121 


153-158 


300 


222 


443 


37-40 


52 


108 


134 


159-162 


303 


223-227 


444 


41-43 


53 


109 


137 


163-164 


304 


228-231 


445 


44-50 


56 


110-112 


144 


165-167 


305 


232 


447 


51 


58 


113 


145 


168 


306 


233 


448 


52-55 


64 


114 


160 


169-172 


308 


234-235 


449 


56-59 


70 


115-116 


161 


173-176 


314 


236 


450 


60-61 


71 


117-118 


165 


177-179 


315 


237-238 


453 


62-65 


72 


119-123 


166 


180-183 


319 


239 


476 


66-67 


73 


124 


168 


184 


320 


240 


486 


68 


74 


125 


171 


185 


321 


241 


487 


69-71 


80 


126 


175 


186 


322 


242 


541 


72-73 


81 


127 


177 


187-188 


325 


243-244 


542 


74-77 


82 


128 


178 


189-191 


326 


245-246 


543 


78-79 


83 


129 


180 


192-193 


332 


247 


550 


80-81 


84 


130 


209 


194-195 


335 


248 


551 


82 


85 


131-133 


210 


196-199 


338 


249-253 


556 


83-84 


87 


134 


211 


200 


339 


254 


557 


85-87 


89 


135 


214 


201-202 


340 







NUMERICAL EXAMPLES IN TEXT 



Number Subject Page 

1 Volume of Wet Steam 70 

2 Volume of Superheated Steam 74 

3 Expansion under Constant Pressure 75 

4 Temperature for a Particular Volume 76 

5, 6 Heat of Steam 81 

7 Internal Energy of Steam 83 

8 Work by the Feed Pump 84 

9 Heat of Superheated Steam . , 87 

10 Heating at Constant Volume 88 

11 Constant-volume Line on Entropy Diagram 91 

12, 13 Adiabatic Expansion of Steam 92 

14 <^arnot Cycle Calculation 101 

15 Rankine Cycle Calculation 105 



CONTENTS. XI 

Number Subject Page 

16 Work per Pound of Steam, Ideal Diagram 110 

17 Steam Jet Calculation 113 

18 Use of Steam Jet Tables 115 

19 Flow of Steam through Orifice 122 

20 Flow of Steam, Special Methods 126 

21 Points on Curves of Constant Total Heat . . . 129 

22 Throttling Calorimeter 134 

23 Use of Calorimeter Diagram 136 

24 Engine Constants 161 

25 Indicated Horse-power 163 

26 Horse-power of Compound Engine 164 

27 Indicated Steam Consumption 167 

28 I.S.C. from Compound-engine Diagrams 168 

29 Steam per Cubic Foot of Displacement 172 

30 Calculation of Missing Steam Quantity 178 

31 Efiiciency of Steam Plant 236 

32 Ideal M.E.P. and Diagram Factor 283 

33, 34 Size of Engine Cylinder 284 

35 Velocities and Accelerations in Engine Mechanism 300 

36 Piston Position, Crank at 90 Deg 302 

37 Angle for Maximum Piston Velocity 304 

38 Inertia Force of Reciprocating Parts 310 

39, 40 Fly-wheel Calculations 321 

41 Stress in Rim of Wheel 325 

42, 43 Reaction of Steam Jet on Nozzle 436 

44 Impulse and Centrifugal Pressure of Jet 438 

45 Calculations for Turbine Stage 446 

46, 47 Ideal Flow through Orifice 453, 455 

48 Flow of Superheated Steam 456 

49 Ideal Energy of Jet 469 

50 Efiiciency by Condition of Jet 471 

51 Calculations for Turbine Test 499 

52 Nozzle Area for Turbine 503 

53 Centrifugal Force at Rim of Turbine Wheel 518 

54 Performance of Steam Blower 538 

55 Performance of Injector 543 

56 Volume of Air and Vapor Mixture 551 

57 Air-pump Capacity 552 

58 Estimate of Probable Vacuum 569 



THE STEAM ENGINE AND TURBINE 



CHAPTER I 
A GENERAL VIEW OF THE SUBJECT 

§ i. The Steam-Power Plant 

(a) A Simple Steam-engine Plant is outlined in Fig. 1, with the 
purpose of showing clearly what are the essential elements or organs 
of a complete apparatus for the generation of power by means of 
heat, derived from the combustion of fuel and utilized through the 
medium of steam. These organs are: 

I The Boiler (including the furnace as well as the boiler proper), 
where the fuel is burned and the steam is generated. 

II The Engine (whether piston engine, as here, or steam turbine), 
in which the expansive force of the steam is applied to the doing of 
useful work. 

III The Condenser, which receives the used or exhaust steam and 
abstracts its heat, bringing it back to the initial state of water. Quite 
frequently the condenser is omitted from the plant, its function being 
taken by the atmosphere, into which the steam is then exhausted. 

IV The Feed Pump, which returns to the boiler either the con- 
densed steam or an equivalent amount of fresh water, thereby com- 
pleting the cycle of operations. 

The boiler and engine are naturally considered the principal mem- 
bers of the plant, while the condenser and feed pump, with the feed- 
water heater, come under the head of auxiliaries. The more important 
parts are named under Fig. 1, and this list of names is to be used in 
connection with the following description of the working of the plant. 

(b) The Function of Combustion. — In the operation of the 
steam generator two distinct sets of phenomena are involved, those of 
combustion and of heat transfer and evaporation. The essential con- 
dition for combustion is that a sufficient supply of air be continually 
brought into contact with the fuel. To secure this, there must be first 



1 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I 





^ S\\\nWC 3ZE^^^ 







Fig. 1. — The Steam Plant. A. Boiler and Feed Pump. 



II 



The Boiler (Water-tube type). 






1. Grate and fire space. 


5. 


Chimney. 


2. Ash pit. 


6. 


Boiler shell or drum. 


3. Hot-gas spaces. 


7. 


Tubes. 


4. Flue and damper. 


8. 


Steam pipe. 


The Engine (Corliss type). 






9. Throttle valve. 


15. 


Crank. 


10. Cylinder. 


16. 


Fly wheel. 


11. Engine frame. 


17. 


Governor. 


12. Piston rod. 


18. 


Exhaust to condenser 


13. Crosshead. 


19. 


Exhaust to open air. 


14. Connecting rod. 







a suitable arrangement for holding the bed of fuel, so formed that air 
can pass through it, with provision made for introducing fresh fuel and 
removing the solid waste products; second, means for regulating the 
supply of air, both below and above the fire, and for producing and 
regulating the draft which draws or forces the air and the combustion 
gases through the fire and along the passages through or around the 
boiler; lastly, a sufficient space above the fire, in which combustible 
gases from the solid fuel can be completely burned before they are cooled 
below the ignition temperature by contact with the relatively cold 
surfaces of the boiler. In Fig. 1, these requirements are met by the 
grate, ash pit, and fire space, with the fire door and ash-pit door, both 
provided with air grids; and by the chimney and damper. With special 
fuels, liquid or gaseous, other arrangements take the place of the grate 



§ 1 (6)] 



THE STEAM-POWER PLANT. 




Fig. 1. — The Steam Plant. B. Engine and Condenser. 



Ill Condenser and Pump (Jet or mixing type). 



20. 


Condensing chamber. 


24. 


Hot well. 


21. 


Cold-water supply. 


25. 


Steam cylinders. 


22. 


Pump cylinders. 


26. 


Steam pipe to pump 


23. 


Discharge pipe. 


27. 


Exhaust pipe. 



IV The Feed Pump (Separate, steam-driven type). 

28. Suction pipe. 30. Steam pipe. 

29. Feed pipe. 31. Exhaust pipe. 

used with solid fuel. And various forced-draft appliances are frequently 
used to assist, or partially to replace, the chimney. 

(c) The Function of Evaporation. — In order that the boiler may 
freely absorb the heat generated by combustion, it must have a large 
area of heating surface, so disposed that there will be a rapid flow of 
the hot gases over the outer side, and that the steam as formed will be 
able to escape freely and rapidly from the inner side. A small pro- 
portion of this surface is exposed to radiant heat from the solid fuel and 
from incandescent flame: this direct heating surface is far more effective 
in absorption than is that which receives heat only by contact and 
conduction from the hot gas. The current of gas is split up into narrow 
streams, and the body of water is likewise divided into small parts, so 
that there shall be only a slight depth of gas acting upon, and of water 



4 A GENERAL VIEW OF THE SUBJECT. [Cha*. I. 

heated by, any particular portion of surface. Whether this intimate 
contact is secured by the water-tube arrangement of Fig. 1, or by the 
fire-tube arrangement of cylindrical boilers, is a matter of minor im- 
portance. Means for insuring a full circulation of the hot gases over 
the whole of the heating surface are shown in Fig. 1 ; and the boiler is 
so formed as to permit free internal circulation, whereby a current of 
mixed water and steam bubbles is continually rising through the front 
connecting tubes into the drum, where there is ample surface for the 
separation of the steam from the water. 

(d) The Boiler a Separate Subject. — The above general con- 
siderations are here stated in full because they are fundamental to an 
understanding of the thermal performance of the boiler, as a member 
of the steam plant. But the boiler is made in so great a variety of 
forms, and there are so many special matters involved in its design, 
construction, and management, that it properly forms a separate sub- 
ject — together with all the appliances for handling and controlling 
steam, such as piping, valves, steam traps, separators, etc. No further 
description of the boiler or of its accessories will be given in this book; 
but a fair working knowledge of these parts of the plant is assumed, 
and reference to their functions will be freely made when the principles 
involved come under discussion. 

(e) The Engine. — Simple representative examples of both the 
piston engine and the turbine engine will be described in this chapter, 
as to form and operation. In general, the engine may be considered 
as a thermodynamic apparatus (involving relations between heat and 
work), and as a machine (involving motions and the action of forces) : 
both these phases of the subject are to be fully developed in this 
treatise. 

(/) Condensing the Exhaust Steam. — The two ways of getting 
rid of the exhaust steam are indicated in Fig. 1. The simplest is, of 
course, open exhaust to the air; but the efficiency of the engine can be 
increased by condensing the steam at low temperature and in a con- 
sequent vacuum, using a pump to remove the water and maintain 
the vacuum. In the figure, the exhaust meets, in the chamber 20, a 
jet of cold water from the pipe 21, and is condensed by direct contact 
and mixing. The water from the condenser, moderately warm, is dis- 
charged to a tank called the hot well. 

The difference here described marks the distinction between con- 
densing and noncondensing engines or plants. A brief description of 
the several types of condensers will be found in Chapter XI. 

(g) The Feed Pump and Feed-water Heater. — In the simplified 
plant in Fig. 1, the feed pump draws from the hot well an amount of 



§ 1 (g)) THE STEAM-POWER PLANT. 5 

water equal to the steam condensed, and forces it directly into the 
boiler, at hot-well temperature; the rest of the warm water runs to 
waste. In a fully developed, well-designed plant of this type, the 
exhaust from the pumps would not go into the main condenser, but 
into a feed-water heater, where perhaps all of its heat can be utilized 
in raising the temperature of the boiler feed. With open exhaust 
(engine noncondensing), and with water drawn from a cold supply, 
the feed-water heater is essential to economy, and should never be 
omitted from the plant — unless controlling conditions inhibit its use, 
as on the locomotive. The matter of heating the feed water is discussed, 
with reference to steam-plant efficiency, in Chapter VI, § 26 (d). 

§ 2. Construction and Working of the Engine 

(a) Representative Examples, of contrasting types of design, are 
shown in Figs. 2 and 3 and further detailed in Figs. 5 to 8. The first 
is of the short-stroke, compact and self-contained, high-speed type; 
the second has a relatively long stroke of piston, is of more drawn-out 
and open form, has the Corliss arrangement of valves and valve gear, 
and runs at a much lower speed of rotation. 

The smaller engine is said to be self-contained . because all of the 
parts, including cylinder and bearings, are carried by the bed and 
sub-base; as appears in Fig. 7, it is of the center-crank form, with two 
main bearings symmetrically located and with two wheels. Even if 
made with a side crank, after the manner of Fig. 8, this engine would 
still be self-contained to the extent of having the cast-iron sub-base 
extend out beneath the outer bearing. In the Corliss engine, the 
cylinder is so long and heavy that it must be fully supported by the 
foundation; and the outer or outboard bearing is independently carried, 
by a pier which extends up from the main base or body of the founda- 
tion. A lighter and more open type of frame is outlined in Fig. 1. 

These are both what are called simple engines, because the steam 
does all its work in one cylinder. The compound engine receives steam 
into a smaller, high-pressure cylinder, and after a part of the work has 
been done the steam passes to a larger, low-pressure cylinder, and thence 
to the exhaust. In some lines of service, this scheme is extended to 
include three or four such successive steps or stages in pressure drop 
and expansion. See § 20, Chapter V. 

(b) The Engine Mechanism, drawn in skeleton outline in Fig. 4, 
consists of three moving members, besides the fixed bed or frame. 
These are, the sliding piece made up of piston, piston rod, and crosshead, 
the connecting rod, and the rotating crank or shaft. The slide, reduced 



6 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 



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8 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 



in Fig. 4 to a simple block around the wrist pin, is the work-receiving 
member, upon which acts the steam force P. Transmitted by the 
connecting rod to the crank pin as R (with some modification), this 
force turns the crank against the external load-resistance. The effect 
of the mechanism is, then, to change from a back-and-forth or recip- 
rocating, straight-line motion of the piece which receives the driving 
force to a rotary motion of the piece which moves against the load 




W 2 ro 2 C 2 

Fig. 4. — The Engine Mechanism, and Principal Driving Forces. 
1. Frame. W. Wrist pin. 



2. Piston slide. 

3. Connecting rod. 

4. Crank. 



C. 
O. 



Crank pin. 
Shaft. 



force. In some types of engines, however, the motion of the piston is 
applied directly to the useful resistance — as in pumps, compressors, 
blowing engines, and steam hammers. 

It is evident from Fig. 4 that the turning effect of the force R will 
be relatively greater when the crank is near the vertical positions OG 
and OH, than when it is near OA and OB. When crank and rod are 
in line, as sketched below the main diagram, the piston being at one 
or the other extreme or limit of its stroke line or travel range, the 
engine is said to be on dead center; in these positions there can be no 
tendency to turn the crank, no matter what force along the stroke line 
or cylinder axis is exerted at W. The essential function of the fly wheel 
or balance wheel is to moderate the wide variations in turning effect, 
and to restrain within a very narrow range the corresponding fluctuations 
in the speed of the shaft. The action of the forces in the machine forms 
the subject of Chapter VII. 

(c) The Piston Slide. — In Fig. 2 the piston is shown as a plain, 
thick disc, made hollow for lightness, but broad of face so as to have a 
liberal bearing surface where it slides within the cylinder. The piston 
of Fig. 3, of more complicated construction, is given in detail in Fig. 206. 
There is a loose fit between cylinder wall and piston, and the joint is 
made steam-tight by the packing rings, which are set into grooves cut 
in the piston rim, and are pressed outward either by their own elasticity 
or by light springs placed beneath them. The piston rod, securely 



§ 2 (c)] CONSTRUCTION AND WORKING OF THE ENGINE. 



9 



fastened into piston and crosshead, passes out of the cylinder through 
a stuffing box, which consists of an annular space filled with a fibrous 
packing material, closely pressed into place around the rod so as to 




Fig. 5 

1. Engine bed. 

2. Bottom guides. 

3. Top guides. 



Engine in Fig. 2) Cross Section at Guides. 

4. Crosshead. 7. Rocker bracket. 

5. Wrist pin. 8. Rocker arm. 

6. Oil guard. 9. Oil tank. 




Fig. 6. — Engine in Fig. 3, Cross Sections, A at middle of guides, B in front of guides, 

both looking toward cylinder. 



1. Engine bed. 

2. Guides. 

3. Crosshead. 

4. Crosshead shoes. 



5. Wrist pin. 

•6. Valve bonnets. 

7. Valve stem. 

8. Wrist plates. 



9. Governor base and 
drive. 

10. Steam rocker. 

11. Exhaust rocker. 



prevent leakage of steam. The crosshead carries the wrist pin, which 
forms the joint with the connecting rod, and guides this pin along its 
straight-line path. The crosshead of Fig. 2, as shown by view A and 
by Fig. 5, has its sliding surfaces on blocks which extend out from the 



10 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 



sides like wings, and requires four guide bars; it is appropriately called 
the wing or four-bar type. In Figs. 3 and 6, the crosshead is of the box 
or trunk type, sliding between guides placed symmetrically above and 
below the axis; the rubbing surfaces are on separate shoes, with wedge 
adjustment to take up wear. 

(d) The Connecting Rod. — It is through the motion of this piece 
that the working force changes from a rectilinear to a circular path. 
Structurally, it consists of the shank or body and two heads which 
carry the bearings for wrist pin and crank pin. The possibility and 



Ji 

m 



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l^mWM 



Fig. 7. — Engine in Fig. 2, Cross Section at Bearings. 



1. 


Engine bed. 


5. 


Oil guard. 


10. 


Counterweights 


2. 


Main bearings. 


6. 


Wrist pin. 


11. 


Plain wheel. 


3. 


Bearing caps. 


7. 


Crank pin. 


12. 


Governor wheel 


4. 


Bearing shell, of babbitt 


8. 


Crank webs. 


13. 


Eccentric pin. 




metal. 


9. 


Shaft, journals. 







method of adjusting these bearings is evident from the drawings. At 
the wrist pin in Fig. 2 there is a bolted strap end, at the crank pin a 
"marine" end; the rod in Fig. 3 has two solid ends. Being subject to 
a violent swinging motion in its plane of movement, the rod of the high- 
speed engine in Fig. 2 has its shank formed with a deep rectangular 
cross section; for low-speed service the rod body is round, as in Fig. 3. 
Piston slide and connecting rod together constitute the reciprocating 
parts of the engine. At high speeds, the inertia forces due to their 
rapid acceleration in alternate directions have a very considerable effect 
upon the force action in the engine. 



2 (e)] CONSTRUCTION AND WORKING OF THE ENGINE. 



11 



(e) Crank Shaft and Wheels. — In Fig. 7 the shaft with inside 
crank is a solid forging, having the crank pin of the same diameter as 
the main journals, and with the counterweights bolted on, as shown 
also in Fig. 2. In Fig. 8 the end crank is built up, the pin is much 
smaller than the shaft, and the counterweight (see dotted outline in 




Fig. 8. — Engine in Fig. 3, Cross Section at Bearings. 



1. 


Engine bed. 


7. 


Bearing shells. 


13. 


Balance wheel. 


2. 


Main bearing cap. 


8. 


Adjusting wedge. 


14. 


Steam eccentric. 


3. 


Bearing shells. 


9. 


Crank pin. 


15. 


Exhaust eccentric 


4. 


Adjusting wedge. 


10. 


Crank disc. 


16. 


Governor pulley. 


5. 


Outboard bearing. 


11. 


Counterweight. 


17. 


Crank-pin oiler. 


6. 


Bearing cap. 


12. 


Shaft. 







Fig. 3) is a part of the cast-iron crank disc ; on account of its length and 
of the very heavy weights which it carries, this shaft is enlarged between 
the bearings. 

The counterweight is put on to "balance" the engine; its centrifugal 
force acts against the inertia force of the reciprocating parts, and thus 
greatly diminishes the free or unbalanced force which tends to shake 
the engine on or with its foundation. See § 30 (g) and § 35. 

Figs. 2 and 7 show belt-pulley wheels, of small diameter and cast 
all in one piece. In Figs. 3 and 8 the wheel (16 ft. in diameter) is made 
in halves, which are held together by heavy bolts at the hub and by 
I-shaped shrink bolts or links at the rim; the deep rectangular rim is of 
the balance-wheel type. The function of the fly wheel, to maintain 
uniformity of rotary speed, has already been alluded to; it is fully 
discussed in § 33. 

(/) Engine Bed and Bearings. — In stationary engines, as here 
illustrated, the frame or body is usually a casting of massive external 
form, but of course made hollow, with ribs or webs to give the needed 
strength and stiffness. Transportation engines, locomotive and marine, 
have a lighter but more complicated structure, to which the name 
framework is more properly applicable. In the engine of Fig. 2 the 
bed, supplemented by light oil guards, forms a casing or inclosure 



1 



12 A GENERAL VIEW OF THE SUBJECT. [Chap. I. 

about the working parts, to retain and collect all the oil that escapes 
from the various bearing surfaces or is splashed from the moving parts. 

The main bearings in Fig. 7 are of unusually simple form, with thin 
shells of Babbitt metal set into place about the journal. In Fig. 8 
(see also Fig. 217) there is vertical adjustment at both bearings, adjust- 
ment at one side of the main bearing for wear, and adjustment at both 
sides of the outboard bearing for alignment of the shaft. 

(g) Lubrication. — The most obvious scheme of oil supply for the 
bearing surfaces of an engine is a set of sight-feed drip cups, on all the 
bearings, to be filled and regulated by hand. A more advanced method 
is to feed oil from a central tank or reservoir, by pipes leading to all 
the bearings, through individual sight-feed nozzles, at which the flow 
can be regulated. Both the engines here illustrated have small oil 
pumps, driven by the valve-gear rocker arms, which return the oil to 
the tank as it runs together after escaping from the bearings; in Fig. 5 
the collecting tank from which the pump draws is shown, beneath the 
rocker bracket. In a large plant, a group of engines or turbines is often 
served from a single installation of this sort, with a separate oil pump, 
oil filters, and a central tank at the low and at the high level. 

To get oil to the crank pin, without the possible need of stopping 
the engine to refill a cup that has run dry, is a problem which called 
for some ingenuity when it was first solved. In Fig. 7, typical of small 
self-contained engines, oil is fed through holes drilled in the solid crank 
shaft; it is collected from the inner ends of the main bearings by annular 
grooves in the outer faces of the crank webs, and is carried to the pin 
by centrifugal force. In Fig. 8 is outlined the device generally used 
on open, side-crank engines; an oil pipe in the form of a return crank 
runs from the crank pin inward to the shaft axis, and at this "fixed 
point" oil can easily be fed into the pipe. 

The lubrication of the internal sliding surfaces of valve and piston 
is effected by using the steam as a vehicle to carry the oil. By means 
of a sight-feed cylinder lubricator, or of an oil pump operated by the 
valve gear, oil of suitable quality is slowly and continually fed into 
the steam pipe close to the steam chest. There it is broken up or 
" atomized," and is carried by the steam (or by moisture in the steam) 
to the rubbing surfaces. In many cases the oil is more directly fed 
upon the admission valves, but even then the steam has a good deal 
to do with its distribution over the valve surfaces, and must still be de- 
pended upon to carry oil to the surface of the cylinder. 

(h) Cylinder and Valve Chest. — Having considered the form 
and working of the engine, as regards its machine action in receiving, 
transmitting, and delivering force, we come next to the question of how 



§ 2 (h)] CONSTRUCTION AND WORKING OF THE ENGINE. 



13 



the primary working force is developed and how it varies; that is, to 
the matter of steam-force action and of steam distribution or the control 
of steam flow. Since all the operations involved are performed within 
the cylinder, this part of the engine is now more fully illustrated in 
Fig. 9, which is especially intended to show the form and arrangement 
of the valve, valve chamber, and steam passages. The simple slide- 
valve engine is taken as the basis of the description of valve action to 
be given presently, all consideration of the more complex Corliss gear 
being reserved for Chapter VIII. Fig. 9 does not belong to the engine 




Fig. 9. — Cylinder with Piston Valve and Inside Admission; A, horizontal section 
along axes; B, cross section at mid-length. 

6. Exhaust spaces and 11. Stuffing box. 
outlets. 12. Gland. 

7. Steam-chest covers. 13. Valve seats. 



1. Cylinder shell. 

2. Cylinder flanges. 

3. Cylinder heads, front 



and back. 

4. Steam ports. 

5. Steam space. 



8. Cylinder sheathing. 

9. Piston. 

10. Piston rod. 



14. Piston valve. 

15. Valve rod. 

16. Stuffing box. 



in Fig. 2 — see Fig. 202 for the valve arrangement of the latter — but 
is of the same class; it has a piston valve, not quite so simple in form 
as the plain flat valve used in Figs. 13 and 14, but the same in effect. 
The central steam space, the steam ports or cylinder ports, and the 
exhaust spaces are clearly enough described by the drawing. The 
throttle valve would be placed just above the steam chest, as in Fig 3; 
and with the two exhaust outlets here shown a special Y pipe must be 
placed beneath the steam chest to make connection with the exhaust 
pipe proper. 

Evidently, a short reciprocating movement of the slide valve, on 
its seat, over the ports, will accomplish the desired end of alternately 



14 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 



admitting steam to, and allowing it to escape from, each end of the 
cylinder. 

(i) The Indicatok and its Diagram. — The performance of the 
steam, controlled by and resultant from the action of the valve, is 
best shown by the steam diagram, of which a typicalexample is given 
in Fig. 11. This is drawn autographic ally by an instrument called the 
steam-engine indicator, illustrated in Fig. 10. The indicator measures 
the rapidly varying pressure in the engine cylinder, and records it in 
terms of piston position; the diagram is on the rectangular coordinate 




Fig. 10. — The Steam-engine Indicator, Crosby design. 

system, with horizontal abscissas showing travel or displacement of 
the engine piston along its stroke line, vertical ordinates showing the 
pressure which existed when the piston was at each successive position. 
By means of a short pipe, with a special shut-off cock which fits 
the union coupling at 6 and 7, the indicator is connected to the cylinder 
of the engine. In Fig. 2 is shown a double pipe connection, with a 
three-way cock, which enables one indicator to serve both ends of the 
cylinder; but it is generally better, and as size and speed of engine in- 






§ 2 (i)] CONSTRUCTION AND WORKING OF THE ENGINE. 



15 



crease it becomes decidedly better, to use separate indicators with 
short and direct pipes. When the indicator cock is opened, steam from 
the engine acts upon the little piston 8 and compresses the spring above 
this piston by an amount proportional to the pressure exerted. The 
pencil mechanism, made up of pieces 13, 14, 15, and 16, magnifies the 
small piston movement and completes the apparatus for measuring 
pressure. The spring is so proportioned that it gives to the pressure 
ordinate a scale of a certain number of pounds per square inch to the 
inch of rise of the pencil at 23. The diagram is drawn on a slip of paper 
carried by the paper drum 24. This drum is moved by a cord, wrapped 
around the pulley 27 and pulling against the spring 31, which is attached 
to a special mechanism driven by the crosshead and so designed as to 
give an exact reduced copy of the motion of the engine piston; then as 
the drum oscillates back and forth upon its axis the paper moves with 
the piston, and the pencil traces the circuit of the diagram. The length 
between perpendiculars, projected on the base line MN in Fig. 11, 




M G Nl 

Fig. 11. — The Steam or Indicator Diagram. 



represents the stroke of the engine, and this line MN, drawn by the 
indicator pencil when steam is shut off, is also the line of atmospheric 
pressure, or the atmosphere line. Ordinates measured from MN, like 
GH, show the difference between the steam pressure on the under side 
of the indicator piston and the atmospheric pressure on the top side. 
When closed to the engine, the indicator cock admits air freely to the 
cylinder of the indicator. 

(j) Action of the Steam. — In considering the form of the indi- 
cator diagram, and the steam action which it shows, we start at the 
point A and follow the curve in the direction ABCDEF. The piston 
being at the beginning (the left end) of its stroke, the valve opens the 
steam port and admits steam to the cylinder, the pressure rising to the 
height MA. This first part of the " admission" fills the clearance 
volume, which is made up of the space left between piston and cylinder 
head (these must not come too close together when the engine is on 



16 A GENERAL VIEW OF THE SUBJECT. [Chap. I. 

dead center) plus the volume of the steam port. As the piston ad- 
vances, the valve being well open, there is. continued admission of steam, 
the pressure keeping up close to that in the boiler; but as the valve 
gradually closes the pressure falls off more or less on account of the 
choking or throttling of the entering current. This action is shown 
by the droop of the admission line AB toward the point of cut-off or 
valve closure at B. With the supply shut off and the piston still ad- 
vancing, the steam in the cylinder " expands," the pressure decreasing 
as the volume increases, according to the expansion curve BC. 

When the piston is at C the port is opened on the exhaust side and 
release begins, the steam escaping gradually as shown by the line CD, 
and dropping almost to the pressure of the atmosphere at the end of 
the stroke. As the piston returns it expels the low-pressure steam 
filling the space ahead of it, until the point is reached at E where the 
valve closes to exhaust; then the steam remaining is compressed into 
the clearance space, its pressure rising along the compression curve EF. 
The exhaust line DE, while generally almost or quite a straight line, 
is always a little above the pressure in the space to which the steam is 
escaping, just as the admission line AB is always below boiler pressure, 
because of the resistance to flow offered by the pipes, valve, and ports. 
In a condensing engine, DE will be well below MN, but yet a little 
above the pressure in the condenser. 

The diagram in Fig. 11 shows the action in one end of the cylinder, 
or the pressure exerted upon one side of the piston; a corresponding 
diagram, reversed right and left, would be obtained from the other end. 

By finding from the steam diagram the average working pressure 
upon the piston, we may calculate the work done or the power developed 
by the engine. 




Fig. 12. — The Valve-gear Mechanism. 
O. Center of shaft. E. Center of eccentric. 

1. Eccentric disc or sheave. 4. Rocker arm. 

2. Eccentric strap. 5. Valve rod. 

3. Eccentric rod. 

(k) The Valve Gear. — In the case of the main engine mechanism, 
we start with the reciprocating piston and transmit work to the rotating 
shaft; to drive the valve, this process is reversed, a reciprocating motion 



§ 2 (k)] CONSTRUCTION AND WORKING OF THE ENGINE. 



17 



being derived from the rotary motion of the shaft. The mechanism is 
essentially the same in both cases, though differing a good deal in the 
form of its parts. 

The driving crank, called the eccentric, has a very short arm or 
throw; and the crank pin, except where it can be placed off the end of 
the shaft, as is done in some center-crank engines like Fig. 7, has to be 
enlarged into an eccentric disc big enough to go around the shaft, as 
shown in Fig. 12. No matter what the size of this disc, the essential 
thing so far as motion is concerned is the position of the center E or the 
length of the radius OE. The eccentric rod is exactly equivalent to 
the connecting rod; but a rocker arm to guide the joint pin V is far 
more usual than a slide block, to which it is practically equivalent. 




Fig. 13. — Relative Positions of Valve and Piston. 

To illustrate the relation between the movements of the two sliding 
pieces in the engine, the piston and the valve, we combine the outlines 
of the two mechanisms in Fig. 13, also turning the section of valve and 
steam passages into this same plane. The simplest form of plain slide 
valve is used in the drawing. Projected on any vertical plane, the 
crank arm OC and the eccentric arm OE form a rigid figure COE, 
which turns about as a fixed center. For any position of the piston 
in the cylinder, or of the wrist pin W on its stroke line MN, we measure 
off WC to locate this crank eccentric, then measure back EV to locate 
the valve. When the subject of valve action is taken up in detail, 
short-cut methods for thus determining relative positions will be 
developed. 

(I) Valve Action. — This is illustrated by Fig. 14, where the work- 
ing of the valve is traced out for a revolution of the engine. In diagram I, 
full lines, the piston is at its extreme left-end position, the crank is on its 
left or head-end dead center, and the valve is open by a small amount, 
so that the steam has a chance to enter and fill the clearance space before 
the piston begins its stroke. As the crank turns in the direction of the 
arrow — right-hand or clockwise rotation — both piston and valve 
move toward the right, until the dotted-line position is reached; here the 



18 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I; 



valve is at the right-end limit of its movement, and the port has its 
fullest opening. The valve now returns, gradually diminishing the 
port opening, until, in the full-line position shown at II, it closes the port 
or cuts off steam. Expansion takes place while the valve moves toward 
the left, the dotted position showing where release is just about to begin. 




Fig. 14. — Valve Movement. 



In III the dotted position shows fullest opening for exhaust; thereafter 
the valve returns toward the right until, as drawn in full lines, it closes 
the port to exhaust and starts the compression. 

Examination will show that the timing of the events in Fig. 14 does 
not correspond with that on the diagram in Fig. 11. 

(m) Governing the Engine. — Any ordinary engine for the genera- 
tion of power must be provided with some automatic device for control- 
ling its running, so as to keep the speed nearly constant. The smaller 
and cruder engines have usually a governor which operates a special 
throttle valve in the supply pipe, and cuts down the working pressure of 
the steam as less power is needed. In all the higher grades of practice, 
however, the governor acts to vary the cut-off, making it later or earlier 
in the stroke as more or less power is called for. 






. 



§ 2 (m) CONSTRUCTION AND WORKING OF THE ENGINE. 



19 



The high-speed type of engine has a shaft governor, of which a good 
example is illustrated in Fig. 15. The eccentric is not fastened upon 
the shaft, but is carried on the swinging piece PQ, pivoted on the wheel 
at P; movement of the center E with reference to the shaft center 




Fig. 15. — The Shaft Governor. 

and the crank arm CO produces the desired variation in cut-off (in a 
manner which is explained in § 39). The controlling device consists of 
the weighted arm FW and the flat-leaf spring at the bottom of the figure. 
The centrifugal force of the weight W acts against the elastic force of 
the spring, transmitted along the steel strap TS. If the load on the 
engine is increased or diminished, it will slow down or speed up until the 
change in centrifugal force causes enough movement of the whole gover- 
nor to accommodate the power of the engine to the new load. The same 
effect of automatically varying the cut-off is secured by the very different 
governor gear of the Corliss engine, as described in § 43. In Fig. 3 is 
shown a second governor, intended to guard against overspeeding. If 
for any reason the main governor fails to control the engine, an increase 
of from five to ten per cent above normal speed will cause the safety 
governor to trip the emergency stop valve, shutting off steam and stop- 
ping the engine. 



20 A GENERAL VIEW OF THE SUBJECT. [Chap. I. 

§ 3. Classification and Characteristics of Engines 

(a) Classification According to Service. — The influence which 
most strongly affects the design and construction of an engine, and from 
which result the most important and essential variations in type, is 
the kind of service for which the engine is intended. On this basis the 
following main divisions suggest and justify themselves: 

1. Stationary Engines for the Generation of Power. — In every case, 
the engine has a rotary load, or the power is delivered through the shaft. 
This power may either be transmitted mechanically (by belt or rope) 
or be first changed into electrical current. For present purposes we 
place an engine which is direct-connected to an electric generator in this 
power class rather than in that which follows. 

2. Directly Loaded Stationary Engines. — The working machine, 
which applies the power of the engine directly to the useful effect (this 
does not describe the electric generator), is closely and intimately 
connected or combined with the engine. Power may be delivered 
through the shaft, as in a mine hoist or a rolling mill, or through the 
piston rod, as in pumps and compressors. 

3. The Locomotive. — With many variations in detail, this conforms 
closely to one prevailing type. 

4. Marine Engines. — In modern practice, and for driving screw 
propellers, these show scarcely any variation in type. 

(6) Other Bases of Classification. — After service, and of 
course largely determined by adaptation to its conditions, come general 
form and arrangement, manner of using the steam, and mechanical 
features. In the matter of steam working, engines may be simple or 
multiple-expansion, as already defined in § 2 (a) ; they may use steam of 
high or low pressure, and either saturated or superheated; and may be 
run either condensing or noncondensing. As to general form and me- 
chanical features, the engine may be horizontal, vertical, or of special 
shape; it may have one of several different styles of framework; and 
may vary quite widely in the number and arrangement of cylinders and 
cranks. Besides the distinction of simple and compound, there is an 
analogous comparison of simple and multiplex arrangements; that is, 
more than one complete engine, whether simple or compound, may be 
combined in one machine, as in a duplex compound locomotive or 
pumping engine. The types of valve gear and of controlling or govern- 
ing apparatus show important differences, and combined with them is 
the question whether the engine runs in but one direction or is reversible. 

To go into the illustration and description of the several types of 
engines and their variations is beyond the scope of this book. A good 



§ 3 (&)] CLASSIFICATION AND CHARACTERISTICS OF ENGINES. 21 

selection of representative examples will be found in The Steam En- 
gine, Chapter VIII, Vol. II. 

(c) The Layout of an Engine. — In order to be able to state con- 
cisely certain important information as to the arrangement of an engine, 
we must adopt conventional terms descriptive of position and direction 
of rotation, as follows: 

Right and Left. — The right side and the left side of a horizontal 
engine are determined by standing back of the cylinder and facing 
toward the shaft. As to what is meant by right-hand and left-hand, 
practice is not uniform; but the writer prefers the scheme of calling the 
side opposite the wheel (in a side-crank engine) the front side, and then 
going by the right and left position of this front. The engine in Figs. 3, 
6, and 8 is thus made " right-hand." In center-crank engines the dis- 
tinction is less marked and of less importance; it is best simply to 
specify on which side the governor is placed, and on which side the 
generator when the engine is direct-connected. 

Over and Under. — A horizontal engine runs over if it makes the 
forward stroke — the piston moving toward the shaft — while the crank 
traverses the upper part of its circle. If we face a right-hand engine 
from the right side, it will have clockwise or right-hand rotation when 
running over. 

In a vertical engine, the front side is properly that toward which the 
crank pin moves when traversing the upper part of its path. Quite 
often the framework is made heavier at the back, especially in marine 
engines; but in many other cases it is practically symmetrical. 



Table 1. Speed Data for " High-speed" Engines. 



Piston stroke. 


Revolutions per minute. 


Feet per minute. 


Inches. 
12 
16 
20 
24 


260 to 300 
210 to 250 
180 to 210 
150 to 180 


520 to 600 
560 to 667 
600 to 700 
600 to 720 



Table 2. Data for Engines of the Corliss Type. 



Piston stroke. 


Revolutions per minute. 


Feet per minute. 


Inches. 






24 


85 to 125 


340 to 500 


30 


80 to 115 


400 to 575 


36 


80 to 110 


480 to 660 


42 


75 to 100 


525 to 700 


48 


70 to 90 


560 to 720 


60 


60 to 75 


600 to 750 



22 A GENERAL VIEW OF THE SUBJECT. [Chap. I. 

(d) Speed of Engines. — This is measured in two ways, by the 
rotative speed or the revolutions per minute, and by the piston speed or 
the distance in feet traveled by the piston in one minute. The data in 
Tables 1 and 2 will give a good idea of the usual range in stationary 
practice. 

It is at once apparent that the distinction between the two classes is 
found chiefly in the rotary speed. Further, the range in piston speed 
(feet per minute) with any particular stroke is greater in the second table 
than in the first ; this is because the Corliss table shows the variation in 
practice extending over a much longer period of time than is covered by 
Table 1. 

Accepting for a convenient basis of comparison the usual range from 
500 to 750 ft. per min., as set forth in the tables, a wider view of practice 
in this matter will yield results about as follows : 

The lowest piston speeds are found in small steam pumps, such as 
are used for boiler feeding. With a stroke of 6 in. or less, the proper num- 
ber of "revolutions" is usually set at 75 per min. as a maximum, making 
the piston speed about 75 ft. per min. For larger pumps of this 
type, the limit is fixed at about 100 ft. per min., while the long-stroke 
pumps without fly-wheel control may rise to 160 ft. per min. Pumping 
engines with fly wheels come next, usually ranging from 120 to 250 ft. 
per min. 

Air compressors run faster than pumps, though not so fast as power 
engines. Piston speeds of 300 to 500 are common, while in very quick- 
running machines as high a figure as 700 ft. per min. may be reached. 

Very large power-house engines go above the limits in the tables, 
speeds of 750 to 900 ft. per min. being common. 

In transportation service, where space and weight are considerations 
of the first importance, the highest speeds are reached. Of course, 
speeds of 500 to 700 are common in the slower types of both steamers 
and locomotives; but for fast and full-speed service 900 to 1000 are 
values often reached and maintained. In very fast locomotives the 
piston speed often rises as high as 1300 to 1400 ft. per min. 

§ 4. The Steam Turbine 

(a) Steam Action in Engine and Turbine. — In the ordinary 
pressure engine, the elastic force of steam is directly applied to the doing 
of useful work, through its action upon the surface of the moving piston. 
The reaction of this working element is just like that of any other part 
of the confining surfaces within the engine, in that it balances the 
internal stress in the steam. The steam force is of the nature of a 



§ 4 (a)] 



THE STEAM TURBINE. 



23 



static pressure, even though it is exerted upon a surface which moves; 
and the engine may properly be said to work on the static-force principle. 
In the turbine, on the other hand, the expansive force is not exerted 
upon an external body, but upon the mass of the steam itself, giving to 
the current or jet a very high velocity. The pressure-work effect is 
changed into kinetic energy, and the latter is usefully applied in one of 
two ways: either the jet is directed from a fixed nozzle upon moving 
curved vanes, in such a way that its resistance to change in direction of 
flow (by the curved surfaces) will act as a driving force to propel the 
vanes; or else the jet is formed within the moving element of the machine 
and the reaction which is opposite to the force accelerating the steam — 
that is, the recoil of the jet — serves as driving force. In either case, 
the turbine works on the dynamic-force principle. 






Fig. 16. — Nozzle and Wheel of the De Laval Turbine. 
View A shows a developed (primarily cylindrical) section 
through the vanes. 



Fig. 17. — Outline of 
an Elementary Re- 
action Wheel. 



The two working schemes just described are illustrated in Figs. 16 
and 17. In the first arrangement — referring especially to view A of 
Fig. 16 — steam of high pressure enters the outer (lower) end of the 
nozzle N, and is expanded to exhaust pressure, the wheel spinning in an 
atmosphere of this low-pressure steam. The action of the jet is obvious, 
and a turbine in which the vanes thus receive the impulse of a fully 
formed jet is said to be of the impulse type. 

In the reaction " wheel" of Fig. 17, steam of working pressure enters 
the hollow rotor at A, and jets are formed in the nozzles B, B; these 
jets blow backward, and their reactions upon the nozzles drive the wheel 
forward. This jet-driven apparatus is then of the purely reaction type. 

(6) The Single-expansion Turbine. — The simplest steam turbine, 
thermodynamically, is that in which the steam drops all the way from 
initial working pressure to exhaust pressure in one operation, or in pass- 
ing through a single nozzle or set of parallel nozzles. The prominent 



24 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 



example of this single-expansion or single-stage type is the De Laval 
turbine, of which the essential form has been outlined in Fig. 16, while 
Fig. 18 shows the section of a complete machine. The nozzles draw 
from the steam chamber B, receiving steam of which the working 
pressure has been fixed by a throttling governor. 

With single expansion the steam jet attains a tremendous velocity — 
something like 2000 to 3000 ft. per sec. — and the Vanes must move 
very rapidly in order to absorb a fair proportion of the kinetic energy of 




Fig. 18. — Section of a 30-horse-power De Laval Turbine, with wheel about 8 in. 
in diameter at 20,000 r.p.m.; vane velocity about 700 ft. per sec. 



A. Turbine wheel. 

B. Steam chamber. 

C. Exhaust chamber. 

D. Wheel shaft. 



E, F. Speed-reducing gears, ratio 

about 10 to 1. 
G. Power shaft. 
H. Governor. 



this jet. In De Laval turbines comparatively small wheels are used, 
practice ranging from a 4-inch wheel at 30,000 r.p.m. to a 30-inch 
wheel at 11,000 r.p.m. To bring these rotary speeds down to some- 
thing practically applicable, toothed gears are used, with very accurately 
cut helical teeth, as partly represented on the larger wheel F in Fig. 18. 
The turbine wheel is mounted on a light, flexible steel shaft, so that it 
will spin without vibration. Fig. 16 is in correct proportion for a 4-inch, 
5 to 7 horse-power wheel, with one nozzle. In the larger sizes a num- 
ber of nozzles are used, up to twelve in the 30-inch, 300-horse-power 
machine, the nozzles being disposed about the circumference of the 
wheel casing. 

Single-stage turbines with a very large wheel and no speed-reducing 



§4(6)] 



THE STEAM TURBINE. 



25 



gearing have been built and successfully operated; but this type has 
never been developed beyond the trial stage, because of the superior 
advantages of the schemes now to be described. 

(c) The Multiple-expansion Turbine. — The first plan that 
presents itself for diminishing the required vane velocity is to cut down 
the velocity of the steam jet. This can be done by dividing the expan- 
sion, or pressure drop, or energy transformation, into a number of steps 
or stages, through the use of a succession of nozzles and vane wheels. 
The scheme is typified by Fig. 19, where the main view is a development 
or flattening-out of a cylindrical section through vanes and nozzles. 

K 90° ; M 



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1 




p IG# 19. — Developed Section of Multiple-stage Impulse Turbine with partial 
peripheral admission; based on high-pressure end of Rateau design, Fig. 20, 
but with rate of expansion or nozzle increase somewhat exaggerated. 

The turbine chamber is divided into a series of cells, in each of which a 
wheel revolves. The first two wheels at the left end of Fig. 20 are 
marked R for "rotor"; and at the same place is shown the hollow, box- 
like construction of the partition discs G, G, which otherwise are cross- 
hatched as if solid, in order to emphasize the difference between their 
bulk and the open space which is filled with steam. There is, of course, 
a running " joint" between each fixed disc and the turbine shaft, which 
is made as nearly steam-tight as possible. 

In Fig. 20, steam enters from the governor valve at A, passes by B to 
C, goes through the first group of wheels to D, and through the second 
group to E; thence a connecting pipe carries it to the low-pressure 
"cylinder" at F, and finally it flows from H to the condenser. The 
valve B is an emergency device, to enable the turbine to meet an over- 
load; when it is opened, there is a larger passage for high-pressure steam 



26 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 



than is afforded by the small nozzle area at C, with a consequent increase 
in steam admitted and power developed, but with some falling off in 
efficiency of operation. 

This example, chosen as an extreme case of subdivision into stages, 
is an early design, and has a larger number of wheels than fuller experience 
has shown to be desirable; and, except in marine service, the idea of 
dividing the turbine into separate sections has generally been given up. 
As in other lines of machinery, the tendency in the development of the 
turbine is toward less complex forms. 

Note how provision is made for increasing the cross area of the steam 
channel as the pressure falls and a current with a certain velocity needs 




Fig. 20. — Section of a 24-stage Rateau Turbine, in three steps and two cylinders ; 
500 horse-power at 2400 r.p.m.; mean diameter of vane rings, 20 in. to 33 in.; 
vane velocity, from 220 to 345 ft. per sec. 




Fig. 20. — Continued. Low-pressure section or cylinder of the turbine, on same 

shaft with high-pressure section. 



more room, because of the expansion of the steam. In Fig. 19 the 
scheme of partial peripheral admission, with increase in width of nozzle 
opening, is shown. The second part of Fig. 20 shows how, after the 
whole circumference has been taken up, the radial dimension of nozzles 
and vanes is progressively increased. 



§ 4 (d)] 



THE STEAM TURBINE. 



27 



(d) The Multiple-impulse Turbine. — In logical sequence, after 
the idea of dividing the operation of jet formation or kinetic-energy 
development into a number of stages comes the scheme of similarly 
dividing the energy absorption or jet application. A typical embodi- 
ment of this idea is shown in Fig. 21. The jet is fully formed in the 




* > V, 



JSBP 
csssr 



<% 



JSBP 

Timm 



•>Vt 



Fig. 21.— Three-impulse Ele- 
ment of a Curtis Turbine. 




Fig. 22. — Diagram of the Nozzle Ad- 
missions in the Curtis Turbine. 



nozzles N; passing through the first vane row Vi, it is discharged into 
the fixed guide vanes Gi, which deflect it back into the proper direction 
for driving, and deliver it upon the second row V2 of moving vanes; 
and after a repetition of this operation the steam is finally discharged 
from the vanes V3. In each set of moving vanes a part of the kinetic 
energy is abstracted from the jet, its velocity being reduced after a 
manner which will be fully explained in Chapter IX. To the parts of 
this process the name " velocity stages" is frequently given, as distin- 
guished from the pressure stages in expansion; but these terms are rather 
awkward for general use, and it seems better to let "stage" stand for a 
pressure-drop division, and to use "impulse" for the action of a jet upon 
any single row of moving vanes. 

The Curtis turbine is the most prominent member of the multiple- 
impulse class. An example is sectioned in Fig. 23, where the general 
form is clearly shown, with much of the larger detail. Each of the 
wheels carries two rows of vanes, instead of the three in Fig. 21. The 
wheel cells are separated by cast-iron diaphragms. The steam supply 
is controlled by valves at the inlet A, while at C is an automatic by- 
pass valve, somewhat similar in function to that at B in Fig. 20. A 
mechanical detail of great importance is the large foot-step bearing 
at F and G, which carries the combined weight of the turbine and 
generator rotors, the electric generator being right above the steam 
turbine. 



28 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 



In Fig. 22 is given a diagram showing the application of the principle 
of partial peripheral admission in this turbine, the nozzle openings being 
represented by the blocked arcs, which are made of decreasing diameter 
in this sketch merely to keep them from overlapping. The initial 
nozzles Ni subtend an arc of perhaps 60°, while the last set N4 (in the 
third diaphragm) covers the whole circumference. The short set Nb in 
the first diaphragm is served by the by-pass valve at C in Fig. 23. 




Fig. 23. — Section of a 2000-kilowatt Curtis Turbine, with four two-impulse stages; 
100-inch wheels at 750 r.p.m.; vane speed about 325 ft. per sec. 

(e) The Reaction Tubbine. — The scheme outlined in Fig. 17 has 
not been developed into a practical steam turbine, because of certain 
inherent disadvantages: it would be rather difficult to introduce steam 
of full pressure into the rotor without undue leakage and friction at the 



§ 4 (e)] THE STEAM TURBINE. 29 

running joint, and the embodiment of pressure staging would be very 
hard to effect. 

The reaction principle finds an extensive application, however, in 
the Parsons turbine, which has very largely preempted the possibilities 
along this line of development. The general arrangement of a typical 

**j 'N **j ^ <*J "N 

mil? 

Fig. 24. — Element of the Parsons Turbine. 

Parsons turbine is shown in Fig. 25, while Fig. 24 gives the shape of the 
vanes or blades. The two most essential features are : first, the mount- 
ing of the blades in a succession of similar rows, alternately on drum- 
shaped rotor and on inside of casing, so as to form a continuous passage 
for the steam, along which its pressure drops progressively and gradually; 
and second, the shape of the vanes, which depart radically from the 
symmetrical profile shown in Figs. 16, 19, and 21. In Fig. 24 the course 
of the steam is from left to right, in a general sense across the vane rows. 
Each set of vanes is formed to receive a current coming squarely in 
sidewise, but to deliver this current, after acceleration, in a direction 
swung well around toward the line of vane movement. Pressure drop 
and acceleration take place in each vane row, whether fixed or moving. 
Speaking approximately, the fixed vanes deliver a current at a velocity 
equal to that of the moving vanes, so that the steam can pass right into 
the channel entrances between the latter; and the moving vanes deliver 
backward steam which leaves the channels with a relative velocity about 
equal (but opposite) to the speed of the vanes themselves, or with an 
absolute velocity of nearly zero. We here refer to component velocity 
in the direction of vane movement, as distinct from the general pro- 
gressive flow across the vane rows, or parallel to the axis of the rotor. 
The whole matter is discussed and graphically exhibited in Chapter IX, 
where it is shown that this turbine is not purely of the reaction type, but 
that there is also some little impulse exerted by the current in entering 
the moving vane rows. 

(/) The Parsons Turbine. — Considering now the general drawing 
in Fig. 25, we note one important characteristic in the enlargement of 



30 



A GENERAL VIEW OF THE SUBJECT. 



[Chap. I. 




QQ 



a 
-u 



n 

o 






5 



o 

02 

o3 

i 

a 

CO 

o 

bD 
.9 

02 



c3 



CI 

.2 

o 
C/2 



CM 

d 
i— i 



the rotor toward the low-pressure end : here the steam flows from right 
to left. This enlargement, together with the increase in vane length, 
provides the necessary increase in cross area of steam channel. On the 
annular side of each step or section there will be a steam pressure which 



§ 4 (/)] 



THE STEAM TURBINE. 



31 



will tend to force the whole rotor toward the left; further, there will be a 
higher pressure on the right or entrance side of each vane row than on 
the left or discharge side, and thus an additional force toward the left. 
To neutralize these forces, the balance discs or " pistons," Pi, P 2 , P3, are 
put on the right end of the rotor, and pressures are equalized through 
the passages Di, D 2 , D 3 . Since but half of the total pressure drop takes 
place in the rotor vanes, the balance-piston diameters extend only to 
mid-length of the vanes. Leakage is minimized by a collar-and-groove 
surface of piston and casing, forming what is called a labyrinth packing 
(see Chapter X). 

The main controlling valve (a double-seated valve of the form II in 
Fig. 280) is at Vi, and normal steam admission at Ai. Under overload 
the by-pass valve V2 opens, and steam enters directly the larger through- 
vane channel at A 2 ; this throws the first step Ri pretty thoroughly out 
of action, its vanes merely churning steam, and there is some consequent 
loss of efficiency. 

(g) Turbines of Mixed Type. — In a Parsons turbine there must 
be a slight clearance between the ends of the blades on one part (rotor 




Fig. 26. — Half Section of the Sulzer Turbine. 



or casing) and the surface of ths other part, for it would not do to have 
actual contact and rubbing. This leaves a passage for leakage from 
stage to stage, which may be of considerable relative amount at the high- 
pressure end of the machine. For this and other reasons, a number of 
composite designs have been developed, of which Fig. 26 is an excellent 
example. There are, first, between A and B, two wheels of the Curtis 



32 A GENERAL VIEW OF THE SUBJECT. [Chap. I. 

type, with two-impulse arrangement; then, from B to C and from D to 
E, there are three groups of Parsons-type blades. These are so placed 
that their end thrusts equalize each other, and no balance-piston device 
is needed. 

The foregoing description is intended to give a general idea of the 
form and working of the principal types of turbines. To sum up, the 
characteristic arrangements are as follows: 

A. One pressure stage and one velocity stage, or the single-stage 
single-impulse turbine. 

B. A number of pressure stages, each with one velocity stage, or 
the many-stage single-impulse turbine. 

C. Several pressure stages, each with several velocity stages, or 
the few-stage multiple-impulse type. Small turbines of this class have 
sometimes but one pressure stage; the common range, however, is from 
two to five stages. 

D. The many-stage reaction type, necessarily without velocity 
staging. 

E. Combinations of type C with B or of C with D. 

The illustrations here, and those in Chapter X — which will show 
some further variations in general form and arrangement, as also the 
details of construction — are from turbines of the stationary type, 
used for driving electric generators. In marine service there are the 
two special requirements of comparatively low speed and of reversi- 
bility. The first is met by increasing the number of stages, whether in 
pressure or in velocity; while for the second an auxiliary section is 
added to the rotor. This backward turbine, of a few stages and hence 
of low-working efficiency, is at the low-pressure end of the main turbine, 
and normally runs idle in an atmosphere of steam of the condenser 
pressure. 

A recent development is the use, on a large scale, of gearing similar to 
that of the De Laval machine. This is being worked out for ship pro- 
pulsion, and has also been tried, with promise of success, for the driv- 
ing of machinery. The gears must be very accurately cut, and the 
difficult requirements are those of quiet running and of durability. 



CHAPTER II 
ELEMENTARY THEORY OF THE HEAT ENGINE 

§ 5. Heat and Work 

(a) Thermodynamics is the science of the relations between thermal 
and mechanical energy, or between heat and work, and is especially con- 
cerned with the transformation of one of these forms of energy into the 
other. This transformation can be made in either direction, and always 
takes place in a fixed and definite quantitative ratio ; but while the whole 
of a given supply of mechanical work can easily be changed into heat, 
it is inherently impossible to convert into work more than a certain pro- 
portion of a given supply of heat. An apparatus for turning heat into 
work is called a heat engine; and the final object of this chapter will be 
to show the manner of operation and to find the limiting performance 
of the best possible heat engine. 

In every such apparatus, heat conversion is effected through the 
agency of an expansive fluid or working medium, which alternately 
expands and contracts as heat is given to and taken from it. Typical 
substances are, air (as representing the dry-gas mixture in engines of 
the internal-combustion class), and steam (or the liquid-to-vapor 
medium). The former follows much the simpler physical laws in its 
behavior, and we will therefore base upon it our primary development 
of thermodynamic ideas and principles. 

(6) Heat is one variety of energy. As existent in sensible* form, in 
material bodies — the form in which it is directly measureable — it is 
believed to consist in a vibratory motion of the molecules of the body, 
and is therefore a sort of kinetic energy. Heat may also be stored in a 
substance in a latent or potential form, as when it changes the sub- 
stance from liquid to vapor. Radiant heat, or the wave action of the 
ether by virtue of which heat traverses space, is of no direct interest in 
thermodynamics. It is assumed that the reader has a working knowl- 

* Sensible heat is that which shows its presence by temperature or its addition 
by raising the temperature of a body: in other words, it is heat that can be felt. 

33 



34 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

edge of the physics of heat, and knows what is meant by radiation, con- 
duction, temperature, specific heat, etc. ; but we now wish to lay renewed 
emphasis upon the two ideas of intensity and quantity of heat. 

Heat intensity is only another name for temperature: the higher 
the temperature of a body, the more rapidly do its molecules move, and 
the more energy do they possess because of this motion. The intensity 
or temperature of a supply of heat is a controlling determinant of its 
availability for transformation into work, as will appear in the develop- 
ment of this discussion. The unit of temperature which we shall use is 
the fahrenheit degree. 

The quantity of sensible heat in a given body, above any chosen 
reference state, depends upon the temperature of the body and its heat 
capacity, the latter being the product of the weight of substance and the 
specific heat or unit capacity. Our practical unit of quantity is the 
British thermal unit or B.t.u., which we shall define as the T ^o P ai *t of 
the heat required to raise one pound of pure water from 32 deg. to 212 
deg. fahr. The pound-degree capacity of any substance (including 
water at various temperatures), measured in terms of this unit, is 
identical with its specific heat. 

The temperature-by-capacity measure of heat is not always directly 
applicable, for under certain conditions large amounts of heat can be 
put into a substance without affecting its temperature. For the con- 
venient representation of thermodynamic operations, it has been found 
necessary to invent another second factor to go with temperature. This 
is called entropy, and its form and use will be brought out presently, 
in § 9. 

(c) Work and Power. — For mechanical purposes, work is to be 
defined as the overcoming of resistance through distance; or, to make 
the action subjective, when a force acts upon a moving body, in the 
direction of the motion and against an equal and opposite resistance, 
it does work upon that body of which the amount is equal to the product 
of force by distance. The common unit of work is the foot pound, the 
work done in overcoming one pound of gravity resistance through one 
foot, or its equivalent. 

Measurement of the work performance of a machine is usually ex- 
pressed, not in terms of absolute work quantity, but rather by the work 
rate, or what is called the " power" of the machine. This brings in the 
element of time, so that if work is defined as force by distance, power 
becomes force by velocity. For small measurements, the foot pound 
per minute or the foot pound per second may be used; for the engine, 
the horse-power or h.p. is the practical unit. This is an arbitrarily 
established rate of 550 ft. lb. per second, or 33,000 ft. lb. per minute, 



§ 5 (c)] HEAT AND WORK. 35 

or 1,980,000 ft. lb. per hour — these numbers all embodying the same 
ratio of work to time. 

For large amounts of work, especially in comparing the work done 
by an engine with heat received, convenient quantity units are derived 
from the horse-power rate, by isolating the output in a unit of time. 
Thus one horse-power in one minute does 33,000 ft. lb. of work, called 
the horse-power-minute or h.p.m. ; similarly, a horse-power- hour or 
h.p.h. is an absolute quantity of 1,980,000 ft. lb. 

(d) Relation Between Heat and Work. — The mechanical equiv- 
alent of heat, or the ratio at which heat and mechanical energy are 
interchanged, is shown by the equation, 

1 B.t.u. = 778 ft. lb. ........ . (1) 

For the number 778 the symbol J is generally used, so that if we have a 
quantity Q of heat energy, its value U in foot pounds will be 

U = 77SQ = JQ (2) 

Conversely, to express work in heat units, we use the letter A for the 
heat equivalent of work, so that 

Q = -L jj = 0.001285 U = AU (3) 

In calculating the efficiency of heat engines, or finding the ratio of 
work done to heat supplied, it is usually most convenient to reduce the 
work output to heat measure; and for this purpose it is well to remember 
that one horse-power-minute is equal to 42.42 B.t.u., and one horse- 
power-hour equal to 2545 B.t.u. 

(e) Thermodynamic Operations. — In every thermodynamic opera- 
tion with an expansive medium, there are two sides or view-points 
from which it may be regarded. One is the mechanical side, with 
pressure and volume as the prominent quantities; the other is the 
thermal side, with emphasis on temperature and heat quantity. In § 7 
(d) it is shown that pressure and volume can be used as factors in work 
quantity, in place of force and distance. In § 9 the idea of entropy is 
developed, with the resulting method of graphical representation of 
thermal quantity. At first we shall approach the subject rather from 
the side of mechanics. 

§ 6. The Perfect Gas. 

(a) The Perfect Gas. — The so-called permanent gases, such as 
hydrogen, oxygen, nitrogen, and air, which un'der ordinary conditions 
are very far from their state of liquefaction, follow very simple laws 
when heated, cooled, expanded, or compressed. Under precise observa- 
tion, however, even these gases show small irregularities and departures 



36 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

from the simple laws. As a basis of fundamental theory, we assume, 
therefore, an ideal, perfect gas. This is supposed to be made up of 
homogeneous and physically indivisible molecules, with no attractive 
forces acting among them, and separated by distances which are exceed- 
ingly large in comparison with their own dimensions. These molecules 
are in constant, free, rapid, rectilinear motion, rebounding with perfect 
elasticity as they impinge upon each other or upon the walls of a confin- 
ing vessel. 

(6) Laws of the Pekfect Gas. — Discovered originally through 
experiment, but later derived mathematically from the physical defini- 
tion just given, the general law of behavior of the perfect gas is expressed 
by the equation p V 

Here p = pressure, measured above the zero of perfect vacuum ; 

v = volume of a given, definite quantity (weight) of the gas; 
T = temperature, measured above what is called the absolute 
zero, which, on the fahrenheit scale, is 460 degrees below the 
ordinary thermometer zero; 
C = a constant. 
From this general, three-variable equation we get simpler relations 
by holding constant, one at a time, the three quantities p, v, and T. 
Thus if p is kept constant, 

± = C or v = CT, (5) 

or, volume and temperature vary together at a constant relative rate. 
Similarly, if volume v is kept constant, 

|=C or p = CT, (6) 

or, volume and temperature vary together at a constant relative rate. 
Finally, if temperature T is kept constant, 

C 
pv = C or p = —) (7) 

or, pressure varies inversely as volume. 

The first two relations, Eqs. (5) and (6), are the two forms of the 
law of Gay Lussac; the third, Eq. (7), is the law of Boyle or of Mariotte. 
It must be understood that the symbol C is here used in the most general 
way, standing for a different value in each of the four equations that 
have been given. 

(c) The Law of Gay Lussac. — Change of volume with tempera- 
ture under constant pressure, Eq. (5), or of pressure with temperature 
at constant volume, Eq. (6), involves, of course, the addition or abstrac- 
tion of heat; and the two operations are generally known as heating (or 



§ 6 (c)] 



THE PERFECT GAS. 



37 



cooling) at constant pressure and at constant volume. At this point, 
however, we consider only the relations between the determining vari- 
ables p, v, and T, deferring all questions as to quantity of heat or work. 
The mechanical side of both operations is represented graphically in 
Fig. 27, where volumes are measured horizontally as abscissas, pressures 
vertically as ordinates. Change at a constant pressure pi from an 
initial volume Vi to a final volume v 2 is shown by the line AB; similarly, 
increase of pressure from pito p 2 at the constant volume V\ is shown by 



4000 



500 



400 




300 



200 



u 

aanaaa 



Fig. 27. — Simple Heating Operations. 

AC. If the body of gas were confined in the cylinder outlined at the 
bottom of the figure, the piston would be allowed to move out against a 
constant resistance in the first case, but would be held fast in the second. 
The line EF, on the volume base OV and with ordinates to the scale 
at the right, shows how temperature rises as volume increases : line GH, 
on the pressure base OP and to the scale at the top of the figure, is a 
similar diagram for the case of heating at constant volume. The rela- 
tion between volume and temperature in one case, and between pressure 
and temperature in the other, is the same, and it will be necessary to 
discuss but one condition. In Fig. 28, temperature is the base, volume 
the ordinate. The part of this diagram from OV toward the right 
represents experimental data: if the volume of a body of gas at freezing 



38 



ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 



point to be taken as unity, the volume at boiling point, after heating 
under constant pressure, will be 1.366; and the law of variation is shown 
by the straight line AC, corresponding with Eq. (5). 

(d) The Absolute Zero. — If now, in Fig. 28, the line AC is ex- 
tended toward the left, it will cut the base line TO at a point Z, which 
is called the absolute zero; and from this point absolute temperature 




Fig. 28. 

is measured. From the relations geometrically set forth in the figure 
we can get a very good concept of the meaning of absolute temperature, 
according to the following line of reasoning: 

Let the temperature of melting ice, 32 deg. fahr., be taken as a natural 
and obvious starting point for temperature measurement. Then the 
triangle ADC or APN shows the ratio, definite and constant, between 
volume increase and temperature rise. Consider now the volume v at 
any temperature t on the thermometer scale: by making the triangle 
ZMN similar to APN, we apply this same ratio to the whole volume. 
It is much simpler to have this whole volume MN or v thus proportional 
to the absolute temperature ZM or T than to have it made up of an 
initial volume MP or v\ and an increment PN proportional to the tem- 
perature rise AP. 

According to Eq. (5) or to the line ZC on Fig. 28, the volume of the 
gas would be nothing at absolute zero. Of course, no actual gas would 
thus shrink to nothing. Rather, it would depart more and more from 
the "perfect" state, and behave as indicated by the dotted profile near 
Z, where the vertical portion L shows liquefaction, followed by a very 
slow contraction with further abstraction of heat. The important fact 
is, however, that over ordinary ranges of temperature the nearly perfect 
gases follow the straight line law AC; and by measuring temperature 
from Z we get much simpler relations than if any other reference point 
were used. 

(e) Absolute Temperature. — Taking from Fig. 28 the proportion 

ZO :OA :: AD : DC, 



§ 6 (e)] THE PERFECT GAS. 39 

letting To stand for ZO or the absolute temperature of freezing point, 
and substituting the numerical values marked on the figure, we have 

To : 180 :: 1.000 : 0.366, 

whence T = 492 deg. This locates the absolute zero at 460 deg. below 
the fahrenheit zero, as stated in the definition under Eq. (4) ; and be- 
tween absolute and thermometer temperature we have the relation, 

T = t + 460 (8) 

(/) The Coefficient of Expansion. — The ratio between the 
volume change per degree and the total volume of the gas is called the 
coefficient of expansion. In general, if we have a volume v at a tem- 
perature T, the gas changes under constant pressure as though it would 
shrink to zero in cooling through T degrees; therefore the ratio* of 
change, which we shall call a, is 

a = \ (9) 

In terms of the volume at any temperature T, this coefficient a is a 
variable, since it is the ratio of the constant increment to the variable 
total volume. To make it a useful constant, we must choose some 
particular volume as a base. Usually, the volume at 32 deg. fahr. is 
taken as unity; then a = 1 -r- 492 = 0.002033; and the same result is 
got by dividing 0.366 jof volume change by 180 deg. — these numbers 
coming from the triangle ADC on Fig. 28. Using symbols as marked 
on that figure, we get very readily the formula 

v = vi[l + a(t -32)]: (10) 

but in most cases it is more convenient to use the relation, from Eq. (5), 

V 2 Vi v 2 T 2 /ni , 

vrri or VrTi (11) 

where the subscripts are used in a general way, to indicate any two 
particular conditions. 

As remarked in the last paragraph of Art. (c), there is no occasion 
for separately developing formulas to cover the operation of heating 
at constant volume; a simple substitution of p for v in Eq. (10) or (11) 
gives all that is needed. 

(g) Mariotte's Law. — Expansion (or compression) at constant 
temperature, Eq. (7), is represented graphically by the curve called the 
equilateral hyperbola, drawn in Fig. 29. If the operation is to be carried 
out in a cylinder with piston, as indicated under Fig. 27, the force along 
the piston rod must vary, always just balancing the pressure of the gas. 

* That is, the ratio of the decrement per degree to the initial volume. 



40 



ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 



Since this curve must frequently be plotted, the most convenient 
construction for finding points upon it is given in Fig. 29. Having the 
reference axes OV and OP (the lines, respectively, of zero pressure and 
zero volume), and a point A through which the curve is to pass, we draw 
through A the lines AD and AE, parallel to OV and OP; then drawing 




E F . V 

Fig. 29. — The Equilateral Hyperbola. 

from the origin any radial line to cut these auxiliary axes at C and D, 
and completing the rectangle ADBC, we determine the point B of the 
curve. For, in the similar triangles DOF, COE, 

DF or AE : CE or BF :: OF : OE, 

or pi : p : : v : v h 

which makes pv = p\V\ and satisfies Eq. (7). 

An operation which takes place at constant temperature is called 
an isothermal operation; and the curve in Fig. 29 is the isothermal 
curve of a perfect gas. 

(h) Formulas for Air. — In order to establish the value of the 
constant C in the equation pv = CT, we must know a full set of coinci- 
dent values of p, v, and T. For the " standard" conditions 

Po = atmospheric pressure, or 14.7 lb. per sq. in., and 
* T = freezing point, or 492 deg. fahr., 

it has been found by experiment that the volume of one pound of air is 

v = 12.385 cu. ft. 
Substituting in Eq. (4) we get, 



C = 



14.7 X 12.385 



= 0.37004; 



492 
whence pv = 0.37 T "" (12) 

The value of C depends, of course, upon the units of measurement used, 
but it is always calculated for the unit of weight, as here the pound. 



§ 6 (h)] THE PERFECT GAS. 41 

The volume of one pound, v in Eq. (12), is called the specific volume of 
the gas. 

Suppose now, as an example, that we wish to see how this specific 
volume is related to the temperature, at the standard atmospheric 
pressure; substituting in Eq. (12) the particular value p = 14.7, we get 

v = 0.025177 7 , (13) 

as the desired formula. 

PROBLEMS 

1. Find the volume of one pound of air under a pressure of 40 lb. per sq. in. 
and at a temperature of 80 deg. fahr. 

2. A receiver of 40 cu. ft. capacity is filled with air at 60 deg. fahr. and a 
pressure of 20 lb. per sq. in. ; what proportion of it must be allowed to escape in 
order that the pressure may remain unchanged when the air is heated to 200 deg.? 

3. Find the coefficient of expansion under constant pressure if the volume 
at 212 deg. fahr. is taken as base. 

4. For a confined body of air, p = 40 lb. and t = 60 deg.; what will p be if 
the temperature is raised to 350 deg., volume being constant? 

5. If a receiver of 32 cu. ft. capacity is filled with air at 80 lb. per sq. in. 
pressure and at 96 deg. fahr., what weight of air does it contain? 

§ 7. Simple Thermodynamic Operations with Gases 

(a) Effects of Heat. — When heat is imparted to an expansive 
substance, with accompanying changes in pressure and volume, there 
are three ways in which the heat may be used or applied; these are, 

First, in changing the temperature of the body: that is, the heat is 
directly stored in the body, in the form of increased thermal or vibratory 
energy of the molecules, without any departure from the sensible con- 
dition. 

Second, in doing internal work within the substance, by overcoming 
molecular attractions. Since such work effects changes in the relative 
positions or arrangements of the molecules, it is called disgregation work. 
In a perfect gas, with no molecular attractions, this element would be 
absent; but when there is a change of physical state, as from liquid to 
vapor, disgregation work is of predominant magnitude. Heat used up 
in this manner changes from the state of active energy to that of passive 
or potential energy; it ceases to be sensible heat, but is ready to reappear 
in that form whenever the conditions are suitable for its escape. 

Third, in doing external work of expansion, by overcoming the 
resistance of the confining surface (of whatever form) through a certain 
distance. The heat thus used definitely ceases to exist as heat, being 
transformed into mechanical work or energy; but it is capable of recon- 
version by a reversal of process. 



42 



ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 



Let / stand for internal work, or change of internal energy, either in 

sensible heat or as disgregation work, or both, and U for external work 

in foot pounds, so that AU is the same quantity reduced to heat units; 

then if Q is a general symbol for heat imparted, we have the fundamental 

equation 

Q = I + AU. . (14) 

We will now consider the thermal relations and quantities involved in 
several of the simplest and most important operations with gases, using 
air as an example and giving numerical values. 



9000 




Fig. 30. — Expansion at Constant Pressure. 

(6) Expansion at Constant Pressure. — In Fig. 30 is represented 
the operation of expanding one pound of air from volume v\ at tempera- 
ture h to v 2 at t 2 , under the pressure p, the external work being shown 
by the shaded rectangle 12BA. The amount of this work can be most 
simply calculated as the product of pressure in pounds per square foot 
by volume change in cubic feet — see Art. (d), following. The pressure 
p being measured in pounds per square inch, this gives 

U = 144p (v 2 - vi) ft. lb.; ' . (15) 

and substituting from Eq. (12) we have 

U = 144 X 0.37 (T 2 - TJ = 53.3 (T 2 - TJ . . . . (16) 

That is, for each degree that the temperature is raised, 53.3 ft. lb. of 
external work is done by the gas, equivalent to 53.3 -r- 778 = 0.0685 
B.t.u. This latter number may well be called, by analogy, the specific 
heat for external work in the particular operation of heating under 
constant pressure. 

In this process, it has been found by experiment that the total amount 
of heat that must be imparted in order to raise one pound of air one degree 
is 0.2375 B.t.u. Using for this specific heat under constant pressure 
the symbol c p , we have 

Q = c p (t s - h) (17) 

as the heat supplied in the operation of Fig. 30. 



§ 7 (6)] THERMODYNAMIC OPERATIONS WITH GASES. 43 

Subtracting from the total specific heat c p the amount expended in 
external work, we get the rate of heat absorption in change of internal 
energy in the gas to be, 

Cv = Cp - 0.0685 = 0.2375 - 0.0685 = 0.1690. . . . (18) 

(c) The Specific Heat for Internal Work, called c v in Eq. (18), 
is also the specific heat at constant volume, because under the latter 
condition the heat supplied does nothing but the internal work of raising 
the temperature of the gas. A most important fact about this internal 
work is that it depends wholly upon the initial and final temperatures, 
and not at all upon the character of the process through which the gas 
passes. No matter what else happens to a perfect gas in a thermody- 
namic operation, the change in internal energy and the heat required to 
produce it is 

J = <v(fr-*i) (19) 

Note that c v is a general constant, while c p and 0.0685 are special con- 
stants, belonging to the operation of heating under constant pressure. 

(d) The Pressure- Volume Measure of Work. — The method 
used in Eq. (15) for calculating mechanical work is based upon the fol- 
lowing considerations: 

If we imagine the body of gas to be enclosed in a cylinder with an 
area of cross section (or of piston) of one square foot, then every cubic 
foot of volume change^ will cause the piston to move one foot, and this 
movement will be against the pressure per square foot, which is 144p 
or P; evidently, then, P(v 2 — Vi) meets literally the definition of work 
as force by distance. As the general case, suppose a piston of area A to 
move the distance S under the pressure P; the work done will be, when 
expressed as force by distance, 

U = PA X S; 
and we need only change the grouping of the factors in order to get 

U = PXAS = P(v 2 -v{), (20) 

or, work = pressure X volume displaced. 

Note particularly that in this pressure-volume method of computing 

work, all measurements must be in terms of the factors of the work 

unit, or must be reduced to those terms. Thus in the foot-pound system, 

pressures must be in pounds and on the square foot, volumes must be 

in cubic feet. For pressure per square foot we shall use the symbol P, 

in all thermodynamic formulas; and for the convenient use of Eq. (12) 

in this connection — as for substitution in Eq. (15) — we give it the 

form 

Pv = 53.3 T = RT (21) 



44 



ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II 



Further, between the two specific heats of air we have the relation 

c v = c p - AR, (22) 

this AR representing for air the number 0.0685, used in Eq. (18). 

(e) The Calculation of External Work. — In the discussion of 
the operation of heating under constant pressure, we derived the internal 
work I from experimentally determined values of Q and A U. Having 
thus established the general expression for I, we follow in other cases 
the method of calculating the external work A U from data as to pressure 
and volume, then adding A U to I in order to get Q. Since pressure now 
varies, the external work must be found by calculating or measuring 
the area under a curve. An example is represented in Fig. 31; and the 
element of work performed during the very small displacement dv, 
which may be considered as taking place at a constant pressure P, is 
shown graphically to be Pdv. The curves used in theoretical discussions 
permit of mathematical integration; those from actual engines, drawn 
by the indicator, must be integrated mechanically, as by the plani- 
meter or by averaging ordinates. Usually, the mean pressure through- 
out a certain volume change is found, whereupon 

U = P m (v 2 -v 1 ); ........ (23) 

but sometimes a work scale per unit of area is used, like that shown in 
Fig. 31, where the unit of base represents 1 cu. ft. and the same unit of 
ordinate 1000 lb. per sq. ft., so that the square unit is 1000 ft. lb. 

(/) Isothermal Expansion. — As stated in § 6 (g), this operation 
takes place, with a perfect gas, under the law Pv = C. Having the 



T=8oo°AF 



5000 




Cu Ft. • 5 |o 

Fig. 31. — The Isothermal Curve. 



relation Pv = Piv h and desiring to integrate Pdv between the limits V\ 
and v 2 which locate the ordinates Al and B2 on Fig. 31, we get P in 
terms of v as 



§7(/)] THERMODYNAMIC OPERATIONS WITH GASES. 45 

whence 



Pdv = P lVl / - = Pi0ilo ge - 
vi J Vl V Vi 



V2 

I rav = r\V\ I - = tr x v\ iog e 
or 



U = Pv loge r (24) 

Here r is the ratio of expansion, always greater than unity (and there- 
fore the inverse ratio of compression), and is equal to v 2 -5- v\ or P x -r- P 2 . 
Substituting from Eq. (21), we have 

U = RT\og e r (25) 

Since there is no change in temperature, no internal work is done, 
and the heat to be supplied, . 

Q = I +AU = + ART \og e r, 

is just equal to the external work done. In the reverse operation of 
compression, work is done upon the gas, and heat must be abstracted 
from it in order to keep the temperature from rising. 

A table of natural or hyperbolic logarithms, for use in this calcula- 
tion, will be found in any good mechanical engineers' handbook. The 
relation to common logs is, 

loge r = 2.3026 log r (26) 

(g) A General Law of Expansion, which has important appli- 
cations, is expressed by the equation 

Pv n = C, ' . (27) 

where the index n takes particular values for different cases. 
With this curve, 

1 



1 — n 

1 
n — 1 
PlVi— P 2 v 2 



dv 



[Pl^l^l 1 "" - P 2 V 2 n V2 1 ~ n ] 

(28) 



n — 1 

Putting this in terms of T, by Eq. (21), and reducing to heat units, 

we have 

AU = AR(T 1 -T 2 ) 

n — 1 

(h) Adiabatic Expansion. — The most important case under the 
above law is the adiabatic* or no-transfer operation, in which no heat 

* The word means, without passing through. 



46 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

is given to or taken from the gas as it expands or is compressed. This 

makes Q equal zero in Eq. (14), whence comes the characteristic relation 

I +AU = 0, or AU = -I ..... . (30) 

In expansion without heat supply, the gas does work at the expense 
of its internal energy and the temperature falls, the negative internal 
work, c v (T 2 — Ti), being just equal in amount to the positive external 
work. This gives the equation 

AR(T 1 -T t ) = .... (31) 

n — 1 

and remembering that AR = c p — c v , Eq. (22), we have 

c p — c v = (n — 1) c v , 
whence 



n = C ^ (32) 

For this particular value of n, 0.2375 -£- 0.1690 = 1.406, the symbol 
k is used. Substituting k in Eq. (28) we get a definite formula for 
external work in terms of mechanical quantities; but generally the 
thermal formula, AU = c y (T*- TJ, (33) 

is more convenient, since the change of temperature is an element of 
major importance in almost any problem that may arise, and hence 
will be calculated for its own sake. 

(i) Adiabatic Temperature Range. — To find the relation be- 
tween the limiting temperatures in an adiabatic expansion from p\V\ 
to P2V2, we proceed as follows: 

The adiabatic pressure-volume equation is 

PiVi k = p 2 V2 k (34) 

Factor this into the form 

P1V1 X vx k - 1 = p 2 v 2 X v 2 k ~ 1 ; 
then substitute from Eq. (21) and get 

RT lVl k ~ l = RT 2 V2 k -\ 
or T 2 /v,\ k ~ l M\ - 406 



(r=w » 



(j) The Adiabatic Curve is drawn in Fig. 32 for a considerable 
range of expansion and of compression, with the isothermal dotted in, 
through a common point A, for comparison. Since the temperature 
drops in adiabatic expansion, the curve AD falls below the isothermal 
AF: at a given volume, as OT, the point N on the adiabatic curve repre- 
sents a lower pressure in the gas than does the point R on the isothermal ; 
and after expansion to a certain pressure, as OS, the gas under isothermal 
conditions fills a larger volume than does that expanded adiabatically. 



§ 7 U)] THERMODYNAMIC OPERATIONS WITH GASES. 



47 



In compression, the external work done upon the gas is changed to 
heat and added to the internal energy, hence the temperature rises, 
and the curve AE goes above AG. Note the temperatures marked 
along the adiabatic curve ED. 



10,000 




5000 



l~ l r I 
CuFt. 



Fig. 32. — The Adiabatic Curve. 

(k) Plotting the Adiabatic Curve. — The task of drawing the 
adiabatic or any other curve of the form pv n = C, if it involved the 
calculation of a set of coordinates directly from the equation, would 





Table 


3. Factors for the 


Adiabatic Curve 




1 


2 


3 


l 


2 


3 


l 

8 


2 


3 


Exp. — 

Vi 


Exp. 


Comp. 


2.25 


0.3198 


0.5617 


0.0537 


0.2274 






2.5 


0.2757 


0.5212 


9 


0.0455 


0.2096 


o V 


V 


V 


2.75 


0.2412 


0.4870 


10 


0.0393 


0.1944 


Comp. — 
Pi 


Pi 


Vi 


3.0 


0.2134 


0.4578 


12 


0.0304 


0.1708 




3.5 

4 


0.1718 
0.1424 


0.4102 
0.3731 


14 
16 


0.0245 
0.0203 


0.1531 


1.125 


0.8476 


0.9196 


0.1392 


1.25 


0.7307 


0.8533 


4.5 


0.1207 


0.3431 


18 


0.0172 


0.1280 


1.5 


0.5655 


0.7495 


5 


0.1041 


0.3183 


20 


0.0148 


0.1188 


1.75 


0.4553 


0.6716 


6 


0.0805 


0.2796 


25 


0.0108 


0.1013 


2.0 


0.3774 


0.6108 


7 


0.0648 


0.2506 


30 


0.0084 


0.0890 



be rather laborious. To facilitate this operation, for the adiabatic of 
air, a series of ratios is given in Table 3, by means of which the ordinates 
can be found by a simple multiplication. In expansion, we take v as 
the independent variable, and locate a series of ordinates to the right 



48 ■ ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

of AB, on Fig. 32, at intervals each equal to one-fourth of the original 
volume vi or CA. Then multiplying the initial pressure AB or p\ by 
the factors in the table, col. 2, we get the lengths of the successive 
ordinates. Thus in Fig. 32 as drawn, AB was 2.665 in., representing 
5330 lb. per sq. ft., which is the pressure exerted when 1 lb. of air is 
confined in a space of 6 cu. ft. at 600 deg. absolute. The distances to be 
measured up from the base line on the successive ordinates were found 
as follows: 

- = 1.25 1.5 1.75 2.0 2.25 2.5 

Vi 

£-= .7307 .5655 .4553 .3774 .3198 .2757 
Pi 

p = 1-947 1.507 1.214 1.006 0.852 0.734 in. 

For compression, p is taken as the independent variable, and volume 
ratios from col. 3 of the table are used. 



PROBLEMS 

1. Let one pound of air at 72 deg. fahr. be heated up to 244 deg. under a 
constant pressure of 20 lb. per sq. in. absolute; find the initial and final volumes 
and the values of total heat, external work, and internal work. Get external 
work first in foot pounds, then in heat units. 

2. A body of air which fills 5 cu. ft. at 100 deg. is heated to 250 deg. under 
a constant pressure of 60 lb. per sq. in. Calculate final volume, external work, 
total heat imparted, and internal work. 

3. A cylinder 2 ft. in diameter and with the piston 1.5 ft. from the cylinder 
head is filled with air at 96 deg. fahr. and 4 atmospheres pressure; what work 
will be done by the air in isothermal expansion to three times the initial vol- 
ume, and how much heat will have to be supplied? 

First compute in terms of mechanical quantities, following Eq. (24); then 
find weight of air present and make a parallel calculation for external work by 
means of Eq. (25). 

4. With the same initial conditions as in Problem 3, let the air be expanded 
adiabatically to the same final volume; what will be the final pressure, the final 
temperature, and the external work done? 

Use Table 3 to get the final pressure. Having this, get external work by 
Eq. (28). After computing T 2) make another calculation of external work by 
Eq. (33). 

5. Compute one of the factors in col. 2 of Table 3, say for an expansion 
ratio of 4. 

6. Following the method of getting Eq. (35), find the similar relation between 
temperature ratio and pressure ratio. 

7. If one pound of air, originally at 680 deg. fahr., and at 100 lb. per 



§7(fc)] THERMODYNAMIC OPERATIONS WITH GASES. 49 

sq. in., is expanded adiabatically to a temperature of 40 deg., what will be the 
final pressure, the initial and final volumes, and the amount of external work done? 
8. If 10 cu. ft. of air at 540 deg. fahr. and 125 lb. per sq. in. is expanded 
adiabatically till the pressure falls to 25 lb., what will be the final temperature 
and volume and the amount of external work done? 



§ 8. The Ideal Heat Engine 

We are now ready to develop the thermodynamic process of the 
ideal heat engine, which is to give the greatest possible efficiency in the 
conversion of heat into mechanical work, and serve as a standard of 
comparison for actual engines. 

(a) The Thermodynamic Cycle. — In every heat engine, the work- 
ing substance goes through a circuit or cycle of operations. Starting 
at a particular condition, it passes through several changes of state, 
returning to the original condition. This continuity of process or 
closure of cycle, either actual or in equivalence, is essential if the working 
of the engine is to be continuous. 

In general, the major divisions of the cycle are, an expansion during 
which heat is received from some source at high temperature and exter- 
nal work is done; and a compression during which external work is 
done upon, or received by, the working medium and heat is rejected 
to an outside body at low temperature. Each of these main divisions 
usually contains two distinct processes, and may contain more than two. 

(6) Positive and Negative Work. — Using the terminology of 
the ordinary cylinder and piston engine, the cycle consists of an out 
or working stroke and a return or compression stroke. Obviously, 
it is desirable that, for a given amount of heat supplied, the effective 
difference between the positive work of expansion and the negative 
work of compression shall be as large as possible, because the ratio of 
this effective work to the heat received measures the efficiency of the 
heat engine. Since the pressure of a given portion of gas, confined in 
a certain space, is proportional to the absolute temperature, and since 
the same range of volumes is passed through in both strokes, the evident 
requirement for high efficiency is that the expansion shall take place 
at the highest possible average temperature and the compression at 
the lowest possible average temperature. 

(c) Working Between Temperature Limits. — The simplest 
conditions as to the supply and rejection of heat are, to have a source of 
heat maintained at a uniform high temperature and a heat absorber or 
cooler kept at a uniform low temperature. With constant temperature 
limits thus fixed, it appears that isothermal operations at the respective 



50 



ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 



temperatures best meet the requirement just stated. But besides 
expansion at a constant high temperature and compression at a constant 
low temperature, there must be a drop from the high to the low tempera- 
ture in one part of the cycle, and a return from the low to the high in 
another. For these operations, the adiabatic process, involving no 
transfer to or from the medium, naturally suggests itself. 




Fig. 33. — The Ideal Heat Engine. 



(d) The Carnot Cycle. — The French scientist Carnot first de- 
vised the cycle made up of two isothermals and two adiabatics. The 
essential apparatus is outlined and the diagram of the cycle given in 
Fig. 33. This ideal engine uses a confined body of air, which is alter- 
nately heated and cooled within the cylinder. All the surfaces in con- 
tact with the air must be thermally neutral, that is, must have zero 
capacity for heat, and all except the cylinder head must be perfectly 
nonconducting; the latter is a perfect conductor, but is provided with 



§ 8 (d)] THE IDEAL HEAT ENGINE. 51 

a removable cover N of the nonconducting material. These require- 
ments as to material — very far from being realized in any actual engine 
— are imposed in order that adiabatic operations may be carried out. 
There is also a source of heat H, or heat reservoir at high temperature, 
and a heat receiver R at low temperature, for the isothermal operations. 
These are of very large capacity, so that they can give off and absorb 
heat without appreciable fluctuation in their own temperatures; and it 
is assumed that heat will pass freely to and from the air when the way is 
opened, without the temperature difference that is really necessary to 
flow of heat. In two respects then, as regards thermal physics, the scheme 
is entirely ideal, representing the unattainable limit toward which the 
actual processes can only approach. Mechanically, provision must be 
made for exerting a force along the piston rod always equal and opposite 
to the pressure of the air upon the piston, and for regulating the move- 
ment of the piston. To carry out the ideal of perfection, it is assumed 
that the machine operates without loss of work by friction. 

(e) The Description of the Cycle shown in Fig. 33, with expres- 
sions for all the quantities involved, is as follows: 

Start at point 1 of the diagram, with a unit weight of air under the 
conditions Pi, v h and T\. 

Phase I of cycle. Heater H on cylinder head, isothermal expansion 
at T h from 1 to 2: pressure-volume relation, 

PlVi = PiV 2 . 

Heat received and work done, 

Qi = AUi= ART ^oge^- 

Vl 

Phase II. Cover N on cylinder head, adiabatic expansion, along 
23, from T x to T 2 : 

P 2 v2 k = iW; 
and from Eq. (35) 

Heat received, 

Work done, 

AU n = c v (Ti-T 2 ). 

Phase III. Cooler R on cylinder head, isothermal compression at 
T 2 , from 3 to 4: 

P3V3 = P A Vi. 

Work received and heat rejected, 

Qiii = At7in = ART, logep- 



vj, (T1V- 1 

V 2 " \T 2 ) 

Qn = 0. 



(36) 



52 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

Phase IV. Cover N on cylinder head, adiabatic compression, along 
41, from T 2 to T x \ 

P 4 V 4 k - p iVl k. 



Vi 



-sr <"» 



Qiv = 0. 



Heat rejected, 

Work received, 

AUiy = c v (T 1 -T 2 ). 

Now from Eqs. (30) and (37), 

v Jl — 2l 

V 2 V! 

whence 

v ^ = ^ = r (38) 

That is, the two isothermal operations, between and limited by the same 
adiabatics, have the same ratio of volumes. 

Now the external works in the two adiabatic phases, Uu and C/rv, 
are equal in amount and balance each other; the effective work is there- 
fore 

U= C/i-C7r I i = ^log e r(7 7 1 -T r 2 ); 

and the ratio of this work to the heat received, or the efficiency of the 

engine, is 

w AU Qi - Qui T 1 - T 2 

With this efficiency, the work gotten out of a given quantity Q of heat 
supplied is, using the factor J, Eq. (2), 

^ U = JQ^^' ....... (40) 

(/) Efficiency of the Ideal Engine. — The result expressed by 
Eq. (39) is of the highest importance, reducing to quantitative terms 
the statement at the beginning of this chapter, that only a portion of any 
given supply of heat can be converted into mechanical work. The 
ideally perfect heat engine, working between the temperature limits 
Ti and T 2 and receiving the heat supply Q, can at the best convert into 
work only the fraction (Ti — T 2 )/Ti of this heat, and must unavoid- 
ably reject as heat the remaining portion, T 2 /Ti. The engine with 
actual imperfections will convert less and reject more than these pro- 
portions. 

It will be noted that while properties of the particular medium enter 
into the detail of the quantitative discussion in Art. (e), these all cancel 
out at the end. Partly from this fact, partly from lines of general 



i 



§ 8 (/)] THE IDEAL HEAT ENGINE. 53 

thermodynamic reasoning which are set forth in § 10, the conclusion 
has been established that the efficiency here deduced is perfectly general, 
being independent of the medium and dependent only upon the realiza- 
tion of the isothermal and adiabatic operations. 

In certain types of heat-engine plants (notably, the common gas 
engine with the explosive cycle), it is inherently impossible to supply 
heat to the working medium, or to reject heat, at anything like uniform 
temperatures. The ideal form of such cycles must be worked out in 
detail, for each case; but a rough measure of the limiting efficiency can 
be got by using the mean temperatures of supply and rejection in the 
ratio of Eq. (39) — this approximation being closer as the operations 
during supply and rejection are more nearly similar. 

Before going on to develop more fully some general principles of the 
heat engine — which can be done in much better fashion after the 
temperature-entropy analysis is made available — we now show the 
utility of the ideal efficiency as a standard of comparison, in the following 
paragraph. 

(g) Absolute and Relative Efficiency. — Suppose that a heat 
engine is found by test to receive a certain amount of heat Q and do an 
amount of work U. The actual ratio of heat converted to heat received, 

, *a-TP («) 

is the absolute thermal efficiency of the engine. The efficiency of an 
ideally perfect engine working within the same limits, or the ideal 
efficiency, is T — T 

The ratio of actual to ideal performance, or the relative efficiency, 

fc-%. (43) 

is the true and proper measure of the effectiveness of the actual apparatus. 
(h) Numerical Example. To show methods of calculation, and 
also in order to bring out certain properties of the Carnot cycle with a 
dry gas (not a vapor, like steam), the particular values belonging to 
the diagram shown in Fig. 33 will now be worked out. 

One pound of air is the medium employed. The primary data are, 

Ti = 800 deg., T 2 = 500 deg., both absolute temperature; 
Vi = 2.5 cu. ft., v 3 = 20 cu. ft. 

Then for phase I, pv = 0.37 7\ = 296, 

and for phase III, pv = 0.37 T 2 = 185. 



54 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

From these general expressions for the respective isothermal curves 

we get 

pi = 296 ^ 2.5 = 118.4 lb. per sq. in., 

and pz = 185 -r- 20 = 9.25 lb. per sq. in. 

The adiabatic ratio is 

i 

r a = (j±f~ ' = (1.6)o^o6 log 1.6 = 0.20412 

loff 1.6 
= 3.182 -^rf = 0.50276. 

0.406 

Now 

v 2 = 20 -7- 3.182 = 6.284, p 2 = 296 4- 6.284 = 47.10 

v, = 2.5 X 3.182 = 7.95, p, = 185 4- 7.95 = 23.27. 

The two isothermal ratios come out as 

5 = 6|84 =2514 ^ 5.V20 =2516 

vi 2.5 Va 7.95 

Using r = 2.515, we get the work of phase I and the heat received as 

Ui = 144p 1 y 1 log e r = 144 X 295 X 0.9223 

= 39,179 ft. lb.; 
Qi = 50.36 B.t.u. 

With the temperature limits given, the efficiency is 0.375; therefore 
the net useful work done by the pound of air is 

39,179 X 0.375 = 14,692 ft. lb. or 18.88 B.t.u. 
The external work of phase II is 

c v {T 1 - T 2 ) = 0.169 X 300 = 50.70 B.t.u. or 39,445 ft. lb. 
The important mechanical quantities for the whole cycle are now, 

Work Mean pressure 

Forward stroke 78,624 ft. lb. 31.20 lb. per sq. in. 

Return stroke 63,932 ft. lb. 25.37 lb. per sq. in. 

Net or effective 14,692 ft. lb. 5.83 lb. per sq. in. 

The mean pressure is got by the method of Eq. (23), or by dividing 
work by piston displacement; the total piston displacement, from v\ 
to v z is 17.5 cu. ft.; and in order to get pressures in pounds per square 
inch, the further divisor 144 must be introduced, so that the work 
quantities are here divided by 17.5 X 144 = 2520. 

(i) Availability of the Carnot Cycle. — These numerical results 
bring out the fact, also made evident graphically in Fig. 33 by the 
extreme vertical narrowness of the cycle diagram as compared with 
its height above the base line, that the net or useful forces are very 
small relative to the total forces acting. Consequently, this is a very 



§ 8 (i)] THE IDEAL HEAT ENGINE. 55 

poor cycle in the mechanical sense, entirely aside from difficulties in the 
way of its thermal realization. In order to embody this cycle, the 
engine must be very large, because of the small useful output per unit 
of cylinder volume, and at the same time very heavy in order to with- 
stand the high pressures acting. Further, friction in the machine will 
be proportional to the big working forces which are so nearly self- 
balanced, not to the small net pressures; and if it bear even a moderate 
ratio to the former, it may absorb an overwhelming proportion of the 
useful work of the latter. For these reasons, the Carnot cycle is not 
available for practical application in the gas engine, but even as, an 
underlying scheme of working must be greatly modified. With steam, 
however, as we shall see presently, it gives a much more effective and 
usable diagram, and with but little modification in intention, it is 
really the basis of the steam-engine cycle. 

PROBLEMS 

1. A heat engine working between the limits Ti = 1000 deg. and T 2 = 
600 deg. absolute receives 9200 B.t.u. per horse-power-hour; what is its absolute 
thermal efficiency and its relative efficiency, compared with the ideal engine? 

2. A steam engine working between the limits ti = 334 deg., U = 112 deg. 
fahr., is six-tenths as efficient as the ideal heat engine; how much heat must it 
receive per minute in order to develop 150 horse-power? 

§ 9. The Temperature-Entropy Analysis 

(a) The Idea of Entropy. — All of the diagrams thus far used to 
represent thermodynamic operations — not including under this head 
the line of temperature relation on Fig. 28 — have shown the mechanical 
side of the subject, leaving the thermal side only implied or understood. 
The natural desire for an equivalent method of representing the opera- 
tion directly in terms of heat, has led to the invention and development 
of the temperature-entropy diagram. As an obvious fact of nature, 
mechanical work is the product of two factors, either force and distance 
or pressure and volume; and if these are made the coordinates of a 
diagram, the area will show their product. For heat energy, tempera- 
ture at once offers itself as one factor; but although specific heat is the 
other factor in ordinary calorimetry, it will not serve as the second 
coordinate of a thermodynamic diagram. Instead, we consider heat 
energy to be a compound quantity, take absolute temperature as one 
factor, and by division find the other factor, to which is given the 
name entropy.* There is no simple physical concept for this quantity, 

* The Greek word means, "a turning toward": it may be paraphrased as "an 
impartation" or "something imparted." 



56 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

but it is not the mere mathematical abstraction that the definition just 
given might imply. It is best, however, to take as foundation the 
mathematical idea, which covers all use of entropy in diagram and 
calculation. A sense of reality and of fuller meaning will grow with 
use and familiarity. 

When a portion of heat Q is imparted to a body at a temperature 
T, the body acquires the entropy N, measured by the quotient 

N = Q (44) 

If the operation takes place with varying temperature, so that only 
the infinitesimal dQ is imparted at any particular temperature T, we 
have 

dRT-^; • (45) 



whence 



whence, during the passage from Ti to T2, the entropy acquired is 

"%= r§. • • (46) 

(b) The Mechanically Simplest Operations first taken up in 
§§6 and 7 — namely, heating at constant pressure and at constant 
volume — both have the essential characteristic that the heat imparted 
bears a. constant ratio to the change in temperature. Letting c stand 
for any constant specific heat, we have 

dN = f = c^; (47) 

XT2/77 7 T 7 T 7 

t£- - e logs 5,?- 2.3026 clog g > . . . (48) 

the last expression being in terms of common logarithms. 

For heating air at constant pressure, c = 0.2375, and Eq. (48) 

becomes T* 

N = 0.54685 log ~\ (49) 

1 1 

while for constant volume the coefficient in Eq. (49) is 

0.1690 X 2.3026 = 0.38914 (50) 

An application of these formulas is seen in Figs. 34 and 35. The 
first shows the same operations as in Fig. 27, with the particular data 
that one pound of air is heated from 492 deg. to 984 deg. absolute in 
each case, so that T 2 /Ti is 2. Always, entropy is abscissa and tem- 
perature is ordinate. While the gas changes state from A to B, the 
entropy acquired is 0.5469 X 0.30103 = 0.1646 = OD; and from A to 
C it is 0.3891 X 0.30103 = 0.1171 = OE. Of course, calculation must 



§ 9 (&)] 



THE TEMPERATURE-ENTROPY ANALYSIS. 



57 



be made for a number of intermediate points in order to lay out either 
curve on Fig. 35. The area under the curve equals the total heat im- 
parted; thus ABDO = Q P = 0.2375 X 492 = 116.85 B.t.u., and ACEO 
= Q v = 0.169 X 492 = 83.15 B.t.u. 



30-, 


p 984° 


C 




20- 










492° 


A 


B 




492° 




984° 


10- 








P- 











v lb 


i 


20 ' 



1000-1 



B 500 



T- 



Fig. 34. — Mechanical Diagram for 
Heating. at Constant Pressure and 
at Constant Volume. 




n o!o5 o:i o:i5 

Fig. 35. — Thermal Curves for 
Operations in Fig. 34. 



100- 




v 10 15 

Fig. 36. — The Carnot Cycle as in Fig. 33. 



20 



i — i — i — i — | — r 
N 0.05 

Fig. 37. — Temperature- 
Entropy Diagram for 
Fig. 36. 



(c) Isothermal and Adiabatic Operations. — In the temperature- 
entropy system, or on the thermal side, the two simplest operations are 
the isothermal and the adiabatic, the elements of the Carnot cycle. 
The first is change of entropy at constant temperature, represented by 



58 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

a horizontal straight line on the diagram; the second is change of tem- 
perature at constant entropy, represented by a vertical line; and the 
TN diagram for the Carnot cycle is the rectangle shown in Fig. 37. 
In the analysis of a thermal operation, these are the ultimate com- 
ponents; for while other operations can be resolved into these com- 
ponents, they themselves cannot be reduced to anything simpler. 

Equation (44) applies to Fig. 37; from 1 to 2 the entropy N = AB 
is acquired by the working medium, the heat received being Qi = NTi 
= area 12BA; the heat rejected in phase III is Q 2 = NT 2 = area 
34 AB, and the heat converted into work is 

AU = N(T 1 -T 2 )=^(T 1 -T 2 ), .... (51) 

i 1 

the same entropy being lost from 3 to 4 that was acquired from 1 to 2. 
Fig. 37 is drawn for the conditions of Fig. 33, which is partly reproduced 
in Fig. 36. The amount of heat received, Qi can be found only from 
the ratio of isothermal expansion, as in the example in § 8 (h), where 
it was calculated to be 50.36 B.t.u. for this particular case; then the 
entropy acquired, AB on Fig. 37, is got by plain division, its value being 
here N = 50.36 4- 800 = 0.063. 

Having set forth the idea of entropy and briefly illustrated how it 
may be applied, we will now use it as a help in some further discussion 
of the Carnot cycle and of the heat engine in general. 

PROBLEMS 

1. In Fig. 35 is represented the heating of one pound of air from 492 deg. 
to 984 deg. absolute. For curve AB (or CD) find value of N at three inter- 
mediate points, at temperatures of 615 deg., 738 deg., and 861 deg. 

2. If Fig. 39 (see forward for description of action represented) shows an 
operation with one pound of air, and the limiting temperatures are T x = 800 
deg., T 2 = 500 deg. absolute, calculate the entropy values BD, BK, and BH. 

§ 10. General Principles of the Heat Engine 

(a) General Thermodynamic Ideas. — Heat energy has an 
active, continual, and irreversible tendency to drop from a higher to 
a lower intensity or temperature. If a hot body is placed in cooler 
surroundings, its intense heat energy tends to escape, diffuse itself, 
and settle to the level of the surroundings. When a body has been 
thus cooled by radiation and conduction, it still retains, at the lower 
level, the heat corresponding to that temperature. 

Instead of simply escaping and diffusing itself, the intense heat 
energy — or we might say, the intense part of it — can be converted 






§ 10 (a)] GENERAL PRINCIPLES OF THE HEAT ENGINE. 59 

into mechanical work by means of a heat engine. Every such device 
takes in heat at high temperature and converts a portion of it; but 
there always remains a residuum, corresponding roughly to what is 
left in a body after simple cooling, which cannot be changed into any- 
thing else, but must be rejected as heat at low temperature. 

The thermodynamic lowering of temperature, through the conver- 
sion of a portion of the supplied heat into work, is a useful process; 
cooling by diffusion is wasteful. For a given range of working, the 
Carnot engine is the most efficient possible because it takes in all its 
supply at the upper limit and rejects all the unused heat at the lower 
limit. If heat is available at a certain intensity, but is received into 
the working medium at a lower temperature (dropping across a tem- 
perature gap), there is evidently a loss of thermodynamic effect; simi- 
larly, if a part of the residual heat is rejected above the temperature 
of the receiver, all of the possible work has not been gotten out of it. 

(6) Thermodynamic Availability. — Suppose that we have a 
heat quantity Qi capable of transfer at T h as, for instance, from the 
constant-temperature reservoir of the Carnot engine. Drawing on 
Fig. 38 the isothermal line AC and making AC or BD equal A\ = Qi/Ti, 
we have the energy Qi diagrammed in the rectangle ACDB; and at first 
we will say that the operation represented is simply the passage of the 
heat Qi from the sourae body, Ni being the entropy given up by that 
body. 

With an ideal heat engine, the line AC will also represent the recep- 
tion of the heat Qi by the working medium; and if the cycle of the engine 
be performed, the heat area ACFE will be converted into mechanical 
work, while the remainder EFDB will be left as residual heat at TV 
For a certain rejection temperature T 2 , the proportion of Qi that is 
available for conversion is greater as 7\ is greater or as Ni is less. At 
the very least, the residual heat will be equal to NiT 2 . 

In general, if a heat supply can be represented graphically, according 
to the temperature-entropy system — the diagram showing its possible 
manner of impartation by the source and of reception by the medium — 
only the area projecting above the level of the lowest temperature attain- 
able in heat rejection can be transformed into work. In simplest state- 
ment, the thermodynamic value of a supply of heat depends upon the 
temperature at which it is available for reception by the heat engine 
(this to be considered in connection with the possible temperature of 
rejection). 

(c) Efficiency in Conversion. — The absolute efficiency of any 
heat engine is greater as the heat rejected to the cooler is less. Assum- 
ing, for convenience (or as the ultimate result), isothermal rejection 






60 



ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 



■Wi- 

-N 2 - 



N„ 



B 



D K 

Fig. 38. — The Limits of 
Heat Conversion. 



H 



at T 2 , and letting Q 2 stand for the heat rejected, we have N 2 = Q2/T2 

as the entropy received by the cooler. Evidently, it is desirable to 

keep N 2 as small as possible. 

In the ideal engine N 2 is equal to Ni; in an actual engine, it 

will be greater, appearing perhaps as BK on Fig. 38, where EJKB 

will then be the area of rejected heat. As 
the extreme opposite to ideal performance, 
let the heat Qi be, through some process, 
simply lowered from Tx to T 2) as by plain 
cooling or "flow" of heat from a hot to a 
cool body: then the final entropy will be 
No = Q1/T2, and area EGHB will be equal 
to ACDB in Fig. 38. If a heat-engine cycle, 
this process will be of zero efficiency, all of 
the available energy, area ACFE, being al- 
lowed to sink below the inferior limit of 
thermodynamic activity, the line EG. 

We see, then, that the limits of heat- 
engine efficiency are, zero on the one hand, 
with maximum increase of entropy from iV\ 
to iVo; and the ideal maximum on the other 
hand, with the cycle between constant 

entropy limits. An increase of entropy from heat reception to heat 

rejection, like FJ, measures the wastefulness of the actual engine, as 

compared with the ideally perfect cycle. 

(d) The Residual Heat. — The general statement at the begin- 
ning of the chapter, that the whole of a given supply of heat cannot be 
converted into work, now takes the form that it is impossible to avoid 
the rejection, as heat at low temperature, of a considerable part of the 
heat received. The amount of this rejected heat we have just been 
considering; a fundamental argument for its unavoidability can be 
very simply expressed in terms of the entropy idea, as follows : 

A body, such as the working medium in the engine, can only gain 
or lose entropy as it receives or gives up heat (not work). In a heat- 
engine cycle, the medium gains entropy with the heat received, and in 
order to return to the starting point it must get rid of this entropy. It 
can do so only by rejecting heat, and even if this be done at the lowest 
temperature, the amount so rejected will be at least N±T 2 . 

(e) The Hydraulic Analogy. — Perhaps the best physical idea 
of entropy can be got by comparing the heat-engine cycle with the 
operation of a water motor, which receives water at a level Hi and dis- 
charges it at a level H 2 (both heights being measured above sea level 



§ 10 (e)] GENERAL PRINCIPLES OF THE HEAT ENGINE. 61 

as an absolute zero). The initial total potential energy of a weight W 
of water is WHi, and at least the energy WH 2 will be left in it when it 
leaves the motor at what is, presumably, the lowest level of discharge 
permitted by the topographical location of the plant. Now the symbol 
W stands for both the force of gravity and the mass or substance quantity 
on which this force acts. We cannot see that entropy is analogous to 
force; but it does correspond quite well with the mass or substance of 
the water. As such an analogue, it may be thought of as a sort of 
energy vehicle, carrying heat energy into or out of a body; and the 
higher the temperature at which it passes from one body to another, 
the more energy does it carry. There is little profit in trying to press 
the analogy into the details of the respective weight-lowering and ther- 
modynamic processes, but the general comparison gives to the concept 
of entropy about as much substantiality as it seems to be capable of 
possessing, in terms of the simpler ideas of mechanics. 

(/) The Idea of Reversibility. — Having elaborated the principle 
of the Carnot cycle, showing more fully that it is the limit of heat-engine 
performance, our next step is to express in simplest yet most compre- 
hensive terms that characteristic of the component operations of this 
cycle by virtue of which maximum conversion of heat into work is 
secured. This characteristic is completely defined by the term " revers- 
ible,'' but the special sense in which that word is now to be used must 
be made clear. 

Consider first the purely mechanical case. To say that a machine 
is, in the present sense, reversible, does not mean merely that it can be 
run backward, but that all the force and work relations can be reversed. 
In a hoisting machine, let the force F be applied to lift a load W; then 
the load W can at any time become a driving force, running the machine 
backward against F as a resistance. For perfect reversibility, the force 
F must be the same in both directions of running; that is, the work by 
F and the work against W must be equal, or the machine must lose no 
work in frictional or other wasteful actions. Reversibility is therefore 
a criterion of mechanical perfection; if it were completely attainable, 
we should have what is called perpetual motion of the first order, in 
which a machine, once started and then let alone, would keep going 
forever. 

This idea is somewhat limited in its applicability in the mechanical 
field, however, since there is a large class of machines which do their 
useful work against a resistance that cannot possibly move backward. 
A locomotive drawing a train on a level track works against the frictional 
resistances to the movement of the train; similarly, a form-changing 
machine, such as any machine tool, has a nonreversible resistance. 



62 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

But even if the concept cannot be formulated from the operation of 
these machines, it is of full effect as a criterion of perfection for them, 
implying as it does that no energy is to be lost within the machine 
itself. 

(g) Reversibility of Process. — Now consider thermodynamic 
processes. On the mechanical side, any operation in which a pressure 
acts upon a movable confining surface, such as a piston, is reversible at 
this surface. If, for instance, a body of gas is expanded at constant 
pressure through a certain range and then compressed under the same 
condition through the same range, the amount of external work, positive 
or negative, will be the same in both cases. With friction in the machine, 
the work which it delivers during the expansion will be less than that 
which it must receive in order to perform the compression — but this 
is outside of the thermodynamic process. 

Whether the heat received during an expansion can, in reversed 
performance of the operation, be put back where it came from, is a much 
larger question. Under Carnot engine conditions — see § 8 (d) — with 
the medium in thermal contact with the source, and with the assumption 
that no temperature difference is needed to make heat pass from one 
body to another, we can easily see that if an isothermal expansion be 
reversed, the heat will return to the source unchanged in quantity and 
state. Under adiabatic conditions, the energy that goes out of the 
medium as work during an expansion very evidently comes right, back 
as heat during compression through the same range. If an operation 
with varying temperature and with heat interchange is to be reversible, 
it is necessary to have a heat reservoir with graded temperature — as, 
for example, a long pipe which is hot at one end and grows cooler toward 
the other — so that each bit of heat can be received or rejected at its 
own temperature. 

Thermal reversibility implies, then, two conditions; first, that the 
medium shall be at the temperature of the source or receiver; second, 
that heat shall pass without a temperature difference to drive it. The 
first may be thermodynamically attainable (except as influenced by the 
second), but the second is physically impossible (just as is a machine 
without friction), although it stands as the limit of the attainable. 

(h) An Irreversible Cycle. — The subject may be clarified, per- 
haps, by discussing a cycle which is entirely lacking in thermal reversi- 
bility. Fig. 39 is, as concerns the outline ACFGHBA, exactly the 
same as Fig. 38, heat being supplied and carried away at the respective 
constant temperatures T ± and T 2 . Now let the gas start at E with the 
temperature T 2 , and be heated at constant pressure up to 7\ at J; 
during this operation, each elementary quantity of heat except the very 



§ 10 (h)] GENERAL PRINCIPLES OF THE HEAT ENGINE. 



63 



T 2 G 

F I 



8 



D K H 

An Irreversible Cycle. 



last will have to drop across the temperature gap from 7\ to the 
instantaneous (variable) temperature T. Reversing the operation me- 
chanically, cool the gas under the same constant pressure, from J back 
to E, rejecting heat to the cooler across the gap from T to T 2 . The 
net result is the mere transfer of a certain 
amount of heat from source to receiver, 
with no useful effect, realizing the zero- 
efficiency case of Fig. 38 and Art. (c). 
The irreversibility of the processes lies in 
the fact that it is impossible to make heat 
pass upward across a temperature gap, so 
that it cannot be put back where it came 
from. Of course, the areas ACDB, EJKB, 
and EGHB are equal. 

Note how the increase in entropy from 
source to receiver occurs. Because of the 
merely diffusive temperature lowering, en- 
tropy BK gained by the medium is greater 
than DB lost by the source; similarly, BH 
gained by the receiver is greater than KB Fig. 39. 
lost by the medium. 

(i) The Reversible Cycle. — To say that the Carnot cycle is 
reversible is in reality only another way of stating that all heat is taken 
in at the upper limit and rejected at the lower limit, but it is a short 
way of making the statement. Further, the Carnot cycle is a particular 
case, with the special requirement of isothermal transfer. The term 
reversible covers arrangements in which heat source and heat receiver 
are not of uniform temperature throughout the operations which they 
control, or in which the temperature limits are not the same for every 
element of the heat used; and in requiring that these limits be 
reached, whatever their form and however determined, reversibility 
becomes a characteristic of the ideal form of the cycle of any heat- 
engine plant. 

(j) The Full Argument from Reversibility, to establish the 
Carnot cycle as the limit of thermodynamic performance — and, by 
inference, any other reversible cycle, with its own particular temperature 
ranges — is as follows : 

Suppose that with the apparatus illustrated in Fig. 33 the cycle is 
performed backward, in the order 14321. During the isothermal ex- 
pansion 43 the heat quantity Ri will be drawn from the cold body at 
T 2 ; to this will be added the effective work AUi of the cycle, and the 
resulting heat, Hi = Ri + AUi will be rejected into the hot body at 



64 ELEMENTARY THEORY OF THE HEAT ENGINE. [Chap. II. 

Ti* The essential fact is that Hi and Ri are respectively the same in 
amount whether the heat engine works directly or reversed. 

Now to drive this reversed engine or heat pump, we employ another 
heat engine, connected to the same source and receiver, drawing from 
the former the heat Hi and rejecting to the latter the heat Ri. If we 
assume that there are no losses of mechanical work, as by friction, the 
second cycle will develop just the work required to drive the first back- 
ward, and the whole combination will embody a self-contained process 
for converting heat into work and then converting it back again. We 
wish to prove that the second engine, of which the manner of operation 
may be anything imaginable within the limits imposed by source and 
receiver, cannot possibly be more efficient than the first reversible engine. 

Since the work quantities are the same 

H 2 - R 2 = Hi - Ri. (52) 

In the first engine, as stated above, the heat quantities Hi and Ri bear 

the same relation to each other and to the work of the cycle in reversed 

as in direct operation; therefore the efficiency when working as an engine 

is 

El = El^} (53) 

Hi 

And the efficiency of engine number two must be 

E % = El=*l (54) 

■CZ2 

Now if it were possible for the second engine to be more efficient than 

the first, we should have 

Hi — R 2 ^ Hi — Ri . /^^\ 

# 2 Hi ' 

this can be true only if Hi is less than Hi, since the numerators of the 
fractions are equal. If Hi were less than Hi, and Ri greater than Ri, 
or if less heat were taken from the high-temperature source than was 
rejected into it, and if more heat were taken from the low-temperature 
receiver than was given to it, there would be a net effect of transferring 
heat from a cold body to a hot body by means of a self-contained proc- 
ess, f According to all our knowledge of the laws of nature, this is 

* This scheme of working finds its practical exemplification in the refrigerating 
machine. 

f The statement of the impossibility of this operation is commonly called the 
second law of thermodynamics; in final and most general terms it expresses and 
accounts for the fact that a heat engine can convert into work only a portion of the 
heat which it receives. The first law is the introductory statement of this chapter, 
that heat and work are interconvertible, in definite ratio. 



§ 10 0')] GENERAL PRINCIPLES OF THE HEAT ENGINE. 65 

absolutely impossible; and we must conclude that the reversible heat 
cycle represents the limit of attainment, toward which the actual engine 
may approach, although it can never reach this limit. 

This argument is, of course, a parallel to the train of ideas summed 
up in Art. (d). A self-propelled transfer of heat from a cold to a hot 
body and a decrease of entropy from source to receiver in a cycle would 
be equivalent effects, either one implying what is called perpetual 
motion of the second order, which means that more energy would be 
got out of a process than was put into it. This is decidedly more im- 
possible than merely to pass energy through a process without any 
diversion from the main channel, which is what the ideal heat engine 
and the frictionless machine are required to do. 



CHAPTER III 
PROPERTIES AND BEHAVIOR OF STEAM 

§ ii. Generation and Properties of Steam 

(a) The Generation of Steam. — The operation of making steam, 
as carried out in the ordinary steam boiler (and regarded from the 
viewpoint of thermal effect), is made up of two parts. The water, 
at some initial temperature U, is pumped into the boiler against the 
internal pressure p; and the first step is the heating of this water up 
to the boiling point t, or to the temperature of steam formation which 
corresponds to the pressure p. The boiling point having been reached, 
evaporation begins; and the water gradually turns into steam, with a 
very great absorption of heat and increase of volume, but with no change 
of temperature so long as the pressure is kept constant by permitting 
a continual discharge of steam, as to an engine. Coming thus from 
the water and in the condition in which it must exist while in the pres- 
ence of water, the steam is said to be saturated, or it is a saturated 
vapor. Conducted away from the water and receiving more heat, 
with rise of temperature, the steam becomes superheated and approaches 
a gas in properties and behavior. Superheating, when performed, is 
to be considered as a third stage in steam formation, following after 
water heating and vaporization. 

(6) Quantitative Values and Relations. — The laws governing 
the perfect gas are rational in character, logically deducible from a few 
fundamental experiments. The corresponding relations for water and 
steam are not thus rational but are almost wholly empirical, in the 
sense that the numerical values of the various quantities had to be 
found by means of a great number of careful experiments, extending 
over the range of variant conditions. The results of these experiments 
are plotted, compared, and combined, and from them are derived laws 
and relations which may or may not be capable of exact mathematical 
formulation. In any case, the formulas are too complicated for ordinary 
use, and for all practical purposes we must depend upon tables and 
diagrams. 

66 






§ 11 (c)] GENERATION AND PROPERTIES OF STEAM. 67 

(c) Steam Tables. — Numerical and graphical tables of the prop- 
erties of steam are given in the Appendix, pages 578 to 615. The 
descriptive list on page 573 defines the ground covered by the several 
tables; the succeeding list of symbols and quantities on pages 574 to 
577 is convenient for immediate reference from the tables, and serves 
to direct further reference back to the descriptions and discussions in 
the present chapter. 

The most general tables, numbers II and III, are carried up to the 
"critical temperature," 689 deg. fahr., above which it is impossible for 
water to exist in the liquid state. To cover the farthest range of at- 
tempted or exceptional use of high-pressure steam, the closely spaced 
part of Table II runs up to 550 deg. or to about 1000 lb. pressure; the 
limit of ordinary technical practice is at about 300 lb. or 420 deg. For 
superheated steam there is a similar liberal extension beyond the limits of 
ordinary practice, Table Diagrams VII and VIII running to 1200 deg., 
while steam is seldom raised above 700 deg. for use in engine or turbine. 

Full descriptions of the quantities tabulated and diagrammed will 
be found in the next two sections. A presentation and discussion of 
the sources of the steam table is beyond the scope of this book, but a 
few notes and the more important references are given in the last section 
of the Appendix. 

§ 12. The Pressure and Volume of Steam 

(a) The Pressure -temperature Relation. — For saturated 
steam, or for the process of vaporization, there is a single, definite rela- 
tion between pressure and temperature, instead of the more general 
relation among pressure, volume, and temperature that holds for a 
gas. If water is subjected to a certain pressure p, it will not boil until 
the temperature t corresponding to that temperature is reached; and 
during vaporization both water and steam remain at this temperature. 
The relation between p and t is given numerical form in Table I and 
in the first two columns of Table II, and is shown graphically in the 
curves Al, A2, and A3 on Fig. 40. At low temperatures the pressure 
is small and varies slowly, at high temperatures it is large and varies 
rapidly; and with a total range from less than 0.1 lb. per sq. in. to 
nearly 3000 lb., there is a real necessity for breaking the pt curve into 
several sections, with different scales for p, as is done in Fig. 40. 

As the temperature of steam falls below 212 deg., its pressure drops 
farther and farther below that of the atmosphere: this fact underlies 
the action of the steam-engine condenser, which is used to diminish the 
back pressure of exhaust steam. 



68 



PROPERTIES AND BEHAVIOR OF STEAM. 



[Chap. III. 



700 



350 



-300 




Cent 



Fahr 



100 PV 200 300 400 500 600 

Fig. 40. — Pressure and Volume Curves for Saturated Steam. 

Vertical base, temperature fahrenheit, with the centigrade scale added at the 

right. 

Curves Al, A2, A3 show the saturation pressure p, plotted from col. 1 of Ta- 
ble II; this is really one curve, but for clearness must be thus broken into sections, 
with a different scale for each as marked along the curve: § 12 (a). 

Curves Bl, B2, B3 show in similar fashion the specific steam volume s, col. 2 
of Table II. To the same scale as B3, the water volume w, Table III, col. 2, 
is laid out in B4, the two curves meeting in a rounded peak at C, at the critical 
temperature: § 12 (c). 

The continuous curve DFKG is a plot of the pressure- volume product, ps for 
steam, pw for water, from cols. 4 and 5 of Table III, to the scale at the bottom of 
the diagram. With this, line DE shows the " ideal " product ps' or RT : § 12 (e). 



§ 12 (a)] 



THE PRESSURE AND VOLUME OF STEAM. 



69 



Most of the properties of steam vary in simpler fashion if developed 
on saturation temperature as a base, rather than on pressure: for this 
reason t is the "argument" or independent variable in Table II, the 
principal steam table. In pract cal observation of steam-plant per- 
formance, however, pressure is commonly the primary quantity; and to 
facilitate the use of Table II, Table I gives the values of t corresponding 
to equally spaced values of p. The necessity here met of a frequent 
change in the p interval shows the chief disadvantage of p as a basal 
quantity for the general table. The fact that a saturation-temperature 
base crowds together the high pressure range (where thermal conditions 
vary slowly with pressure), and spreads out the low-pressure range 
(where they vary rapidly), is the reason for making this temperature 
the determinant in diagrams where pressure is distinctly the funda- 
mental quantity. This remark applies especially to the curves in Figs. 
46 and 48 and in Table VIII, each of which is for a particular (constant) 
value of p and extends out from saturation into the region of superheat, 
and which are nevertheless located by starting points at ten-degree 
positions on the saturation line. . 

(6) Measurement of Pressure. — Up to this point we have taken 
p to be absolute pressure, measured above zero or from a state of perfect 
vacuum (and shall continue to do so unless otherwise stated) . All ordi- 
nary pressure gages, however, measure from atmosphere as a starting 
point, whether upward as on a boiler or downward as on a condenser. 

Table 4. Pressure-unit Ratios. 



1 lb. per sq. in. 

1 lb. per sq. ft. 

1 atmo. 

1 inch mere. 

1 mm. mere. 

1 kg. per sq. cm. 

1 kg. per sq. m. 



Lb. per 
sq. in. 



1.00 
00694 
14.697 
0.4912 
.01934 
14.223 
.00142 



Lb. per 

sq. ft. 



144 
1.00 
2116.4 
66.33 

2.785 

2048.1 

0.205 



Atmos- 
phere 



06804 



1.00 
.03342 



0.9677 



Inches 
mere. 



2.036 
.0141 
29.92 
1.00 
.0394 
28.95 
.0029 



Mm. mere. 



51.71 
0.359 
760 
25.40 
1.00 
735.4 
.07354 



Kg. per 
sq. cm. 



07031 



1.0334 
.00345 
00136 
1.00 
0.001 



Kg. per 
sq. m. 



703.1 

4.8825 

10.334 

34.54 

13.60 

10,000 

1.00 



To use this table, take the name of the first unit in the column at the left and 
run along its line till the value in terms of the other unit is reached, in the column 
headed by the name of that unit. These ratios can be selected in pairs which are 
reciprocals of each other; the values left blank are reciprocals of large numbers, 
and would require too much space because so many zeros precede the significant 
figures. 

To their indications must be added either the normal atmosphere, 14.7 
lbs. per sq. in., or, in more precise work, the actual barometric reading 
at the particular time and place. Numerically, the reading of a vacuum 



70 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 

gage is subtracted from the reading of the barometer in order to get the 
absolute pressure in the condenser. Vacuum gages, from their analogy 
to the barometer in range and because of the former common use of the 
mercury manometer in this service, are generally graduated in inches 
of mercury column. 

In the metric-centigrade countries, the common unit of pressure is 
the kilogram per square centimeter; while for work calculation kilo- 
grams per square meter correspond to pounds per square inch. Ratios 
of equivalence among the various pressure units are given in" Table 4. 

(c) Specific Volume and Density. — For volume we shall use 
three symbols; in general, v will represent the volume of one pound of 
substance in cubic feet, under any conditions; in particular, w will be 
the volume of one pound of water and s the volume of one pound of 
saturated steam. For density, which is the reciprocal of specific volume, 
showing weight per cubic foot, we shall use d w for water and d a for 
saturated steam. The volume and density of water are given in Table 
III, cols. 2 and 3. Steam volume s fills col. 2 of Table II, but d 3 is not 
tabulated. In Fig. 40, s is plotted after the same manner as p, in the 
curves marked B ; and to the very large scale of the upper section B3 is 
laid out also the water volume w in curve B4, these two curves meeting 
in a rounded peak at the critical " point" C. 

{d) Volume in Partial Vaporization. — As indicated in § 11 (a), 

the process of vaporization (under constant pressure) begins with one 

pound of water at t and p and ends with one pound of steam at the same 

temperature and pressure. During the operation the volume changes 

from w to s; for the increase of volume we use the symbol u, so that 

u = s — w. . . (56) 

The proportion of the volume change u that has been effected at any 

point in the process is the same as the proportion of the pound of water 

that has been turned into steam. If x be the proportion or fraction of 

steam (by weight) at any instant, and (1 — x) or m the fraction of water 

or moisture, the volume will be either 

v = w + xu, (57) 

or 

v = s — mu (58) 

In many cases, when x is large or m small, it is quite accurate enough 

to use v = xs (59) 

This is especially appropriate at low or moderate pressures, where the 
difference between u and s is relatively insignificant. 

Example 1. — If one pound of water be 60 per cent vaporized at a pres- 
sure of 100 lb. absolute, what space will it occupy? 

By Table I the temperature is 327.86 deg. From Table III, w is 0.0177 



§ 12 (d)] THE PRESSURE AND VOLUME OF STEAM. 71 

or 0.018, and from Table II, s is 4.430; then u is 4.412, and for v we have either 

v = 0.018 + 0.6 X 4.412 = 0.018 + 2.647 = 2.665 cu. ft., 
or 

v = 4.430 - 0.4 X 4.412 = 4.430 - 1.765 = 2.665 cu. ft. 

(e) The Pressure-volume Product. — More useful than the 
simple plot of volume on temperature (curve B1-B2-B3, Fig. 40), as x 
a help in studying the properties of steam and to show how actual 
steam differs from a perfect gas in behavior, is the diagram got by plot- 
ting the product pv on t. This also is shown in Fig. 40, ps by the curve 
DFK, pw by GK. Values of these products are given in Table III, 
cols. 4 and 5. The straight line DE shows how the product pv would 
vary with t if the steam were a perfect gas. It represents the equation 

pv = RT, (60) 

and for H 2 gas, on the basis of molecular weight, the value of R would 
be 0.5956 — compare 0.37 for air, Eq. (12). 

(/) The Saturation Line. — The curve showing the volumetric 
condition of steam which is completely vaporized but not at all super- 
heated, whether s on t, s on p, or ps on t or p, is called the saturation 
line. When approached from the side of a steam-and-water mixture 
or of wet steam, it might better be called the dry-steam curve. As 
the limit of any operation of cooling from a superheated condition, 
showing where further abstraction of heat will begin to cause conden- 
sation, it is closely described by the term saturation line. In any case, 
the curve stands out as a boundary line between these two general 
states. 

(g) The Ideal Volume of Steam. — As steam is more highly 
superheated, it comes nearer and nearer to the simple law expressed 
by Eq. (60): but toward saturation there is a shrinkage of volume or 
a decrease in the value of pv, shown in its full effect by the inward bend- 
ing of the curve DF from the straight line DE on Fig. 40. This shrink- 
age is inappreciable at very low pressures, but becomes greater as the 
pressure is higher and the steam more dense. The molecules being 
crowded closer together, their inter-attractions become of considerable 
magnitude; and it is thought that even before the point of actual con- 
densation is reached, the molecules may begin to coalesce in small 
groups. 

By evaluating Eq. (60) for the coincident pressure and temperature 

of saturation, we get the " ideal" value of s for these conditions: the 

operation is, n 5956 

s , = ihoyoo ( ^ + 459 >6) * 61) 

V 
* This more precise value is used in making calculations for the tables, instead 
of the even 460 deg. 



72 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 

The results of this computation are given in col. 3 of Table II — 
not for illustrative purposes, but as a help in getting the volume of 
superheated steam at any pressure and temperature. The difference 
(Y — s) ranges from 1.3 cu. ft. at 32 deg. to 0.145 cu. ft. at 550 deg.; 
but while its absolute value is small and decreasing, its relative impor- 
tance increases rapidly, as appears from the following figures, namely, 
that at 32 deg. the difference is 0.04 per cent of s, at 212 deg. it is 1.65 
per cent, at 400 deg. 10.8 per cent, and at 550 deg. 34 per cent. 

(h) The Characteristic Equation. — The general pressure- 
volume-temperature equation for steam at and beyond the state of 

complete vaporization is, 

pv = RT-F p f t , (62) 

where F p and f t are functions of pressure and of temperature respec- 
tively, and their product serves as a corrective term, to change from 
the ideal to the actual value of pv. These factors are determined by 
conditions at the saturation line, as follows: 

For the various temperatures in col. of Table III, values -of RT 
or of [0.5956 (t + 459.6)] were computed, and from them were sub- 
tracted the values of ps given in col. 5, to get (RT — ps), which is 
equal to F p f t . Following Linde — see note 4, page 616, Appendix — 
the pressure factor F p is taken as 

F =*, + .£., ....... . (63) 

p p ^700 

of which the calculated values are not printed. Then division of 
(RT — ps) by F p and interpolation give f t as in col. 5 of Table II. 
Above 535 deg. there is a change in method, f t being assumed and F p . 
derived from it by the same operation of division. High-range values 
of ft, from 600 deg. to 1300 deg. fahr., are given in Table IV. 

(i) The Volume of Superheated Steam. — Cols. 3, 4, and 5 of 
Table II contain numbers to be used in getting the volume of steam 
at any pressure and temperature, by a method more convenient for 
regular use than the direct evaluation of Eq. (62). First, divide both 
members of Eq. (62) by p; the resulting expression for v is 

«-fr -£7, -•-/,/. (64) 

Here v' is the ideal volume, under Eq. (60), and the product f p f t 
diminishes it to the actual volume. The factor f p is, from Eq. (63), 

f = F JL= l + -£-'; (65) 

Jp p ^700 

it is not tabulated — except in Table V, above the range of this for- 



§ 12 (*)] THE PRESSURE AND VOLUME OF STEAM. 



73 



mula — because to write it out from the formula is at least as easy as 
to interpolate in a table which has temperature as argument. 

It is best to think of volume v as reached by a constant-pressure 
expansion from saturation temperature t a (plain t in the tables) to exist- 
ing temperature t; then the easiest way to get the ideal volume v' is to 
take it as 



„' = s ' + !#_y 



This is preferable to the operation 

R 



v' = - (t + 459.6) 
V 



(66) 



(67) 



because, with the usual range of not very great superheat, the quantity 

(v f — s') = — (t — t s ) can be computed closely enough with the slide 

rule, but in order to get the whole of v' from T we must use more precise 
methods of arithmetic. 




5 3.0 V 3.5 4.0 45 

Fig. 41. — Method of Calculating the Specific Volume of Superheated Steam. 

The scheme of this calculation is represented in Fig. 41. Satu- 
ration volume s is plotted in curve FG, which is therefore the saturation 
line, and the ideal volume s' in curve HK. At 150 lb. pressure — 
assuming conditions as in Example 2 — AB is the value of (s' — s), or 
of fpft at saturation temperature. Having s' at B, we compute (v' — s') 



74 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 

in order to get v' at C, then subtract f p f t as computed for the temperature 
at line CD. 

With the high-range values of f p in Table V is given a quantity 
called Af p ; this is the difference between f p as tabulated and the value 
got from Eq. (65) for the determining pressure. To get intermediate 
values of f p , interpolate Af p and add it to the number given by Eq. (65). 
Thus at 980 lbs. we should have 2.4000 from the formula and 0.0029 
for Af p , giving 2.4029 for f p . If a high degree of consistency is desired 
a curve of Af p can be plotted, instead of using plain, straight-line 
interpolation. 

Example 2. — Find the volume of one pound of steam at 150 lb. absolute 
and at 500 deg. fahr. 

For p = 150, t s = 358.5, from Table I; then by Table II, s = 3.016, s' = 
3.249, R/p = 0.003970, f p = 1.214; at 500 deg., f t = 0.080, (t - t s ) = 141.5. 

s' =3.249 v' = 3.811 

- (t - ts) = 0.562 f p f t = 0.097 

V 

^ = 3.811 v = 3.714 

In Table VI this volume can be read as 3.71 cu. ft., which would be quite 
close enough for most purposes; the disadvantage of that diagram is the im- 
possibility of close interpolation on pressure lines other than those which are 
drawn in and divided. 

(j) Expansion Under Constant Pressure. — Fig. 41 shows the 
change of volume with temperature under constant pressure. Coming 
down from high superheat, the ideal line CB would keep straight on 
till it crossed the vertical axis of temperature, here five divisions beyond 
the left edge of the diagram, at absolute zero. The actual line DA 
swings inward, v contracting more rapidly than v', until it gets to satu- 
ration at A; then, with condensation taking place, v contracts along 
the isothermal line AE to the water volume w. 

The rate of change of volume with temperature under constant 

pressure, defined mathematically as ( -r:) , is of interest. For the ideal 

gas, as readily appears from Eq. (60) , it is — ; for actual steam it is, 

from Eq. (64), 

%l (68) 

at 



dv\ R_ f 

dt) p V h 



The last term is the rate of change in f t per degree; it is negative, so 
that the term is really additive, and it can be accurately enough got 
from Table II. 



§ 12 (j)] 



THE PRESSURE AND VOLUME OF STEAM. 



75 



Example 3. — For the conditions of Fig. 41 and Example 2, find the rate 
of expansion at 500 deg., and at saturation. Also, find where tangents to the 
curve AD will cut the temperature axis in each case. 

In passing 500 deg., ft changes from 0.0827 at 495 deg. to 0.0775 at 505 deg., 
or at the rate of —0.00052 per degree; multiplying this by f p or 1.21, we get 
0.00063 to be added to R/p or to 0.00397, making the rate of change 0.00460 
cu. ft. per degree. At 358.5 deg., the rate of change in f t is —0.00112, and the 
rate of expansion is 0.00397 + 0.00124 = 0.00521. 

Now at 500 deg., the volume of the pound of steam is, from Example 2, 3.714 
cu. ft.; to reduce this to zero at the rate of 0.00460 per degree would require 
a drop of 3.714 -=- 0.0046 = 807.4 degrees. The absolute temperature at D, 
Fig. 41, is 959.6 deg., so that a line tangent to the curve AD at D will cross the 
axis of temperature or the line of zero volume at 959.6 —807.4 = 152.2 deg. ab- 
solute. Similarly, at 358.5 deg., 3.016 -f- 0.00521 =578.9, the absolute tempera- 
ture is 818.1 deg., and the tangent crosses at 818.1—578.9 =249.2 deg. absolute. 

(k) Variation in Rate of Expansion. — The example just worked 
clearly exhibits the fact that the rate of expansion under constant 
pressure is greater near saturation than farther out. The inverse of 
this, that the rise of temperature required for a certain increment of 
volume is less near saturation, is equally clear on Table-diagram VI. 
The divisions on the horizontal lines of constant pressure mark off 
temperature intervals corresponding to equal changes of volume. Near 
saturation, the intervals are appreciably shorter, especially at high 
pressures. 

r 400 t 500 DEG. 600FAHR.700 800 900 1000 

\i I ■ ' I l_ J ' ' ■ ..'..' ..'..' i . Q 




111111(111111111111 

3 v 3.5 Cu. 4 Ft. 4.5 



I i i ' 



""3 



Fig. 42. 



5' 5.5 

Temperature Intervals for Volume Increments of 0.1 cu. ft., 
at 150 lb. Pressure. 



To show this up more strongly, the diagram in Fig. 42 is plotted, 
for the pressure used in the last two examples. The ordinate between 
base AA and curve BB is the number of degrees required to change 
the volume by 0.1 cu. ft. These ordinates are located, with reference 
to the actual volume, by the scale along the bottom, each at the middle 
of the increment which it produces; and at the top is a variant scale of 
corresponding temperatures. The height from AA to CB is the value 
(constant) which the temperature interval would have if the steam 
followed the law of Eq. (60) : the actual intervals approach this limit, 



76 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 

becoming indistinguishable from it, on the diagram, at high tempera- 
tures. To get AC, divide the volume increment 0.1 by the ideal rate of 
expansion, R/p; then 

Ac: °- lx I = 2 iiS- = 25 - 02d ^ 

(I) To Find the Temperature which, under a certain pressure p, 
corresponds to a particular volume v, is a troublesome operation with 
the data in Table II; since f t depends upon the final, unknown tem- 
perature, a series of trial solutions is necessary, each based upon the 
one ahead of it and coming closer to the true result. Table VI gives 
just this quantity, however, and if the precision with which it can be 
read is insufficient, at least furnishes a close approximation upon which 
to base a single corrective calculation. An example will illustrate the 
procedure to be followed. 

Example 4. — Under a pressure of 180 lb., find the temperature at which 
one pound of steam will fill a space of 3 cu. ft. 

On the 180-lb. line, Table VI, the reading for 3 cu. ft. is about 481 deg. 
The saturation temperature being 373.15 deg., Table II gives s' = 2.755, R/p = 
0.003309; at 481 deg., t - t s = 107.8, and f t = 0.0903; at 180 lb., f p = 1.257. 
Now making the same calculation as in Example 2, we have 

s' = 2.755 v' = 3.1117 

- (t - t s ) = 0.3567 f p f t = 0.1134 

V . 

v' = 3.1117 v = 2.9983 

This makes the volume 0.0017 cu. ft. less than the desired 3 cu. ft. With 
R/p equal to 0.00331, the needed increase will be produced by a rise of 0.0017 — 
0.0033 = 0.5 deg., so that the exact temperature sought is 481.5 deg. instead of 
481 deg. It must be noted that because f t changes with t, this last simple cor- 
rection can be made over but a very short distance; if the difference between t 
from Table VI and t as just computed had been even as great as one or two 
degrees, a second calculation would be necessary in order to fix t within 0.1 deg. 

(m) Heating at Constant Volume. — Sample curves for this 
operation with one pound of superheated steam, in a simple plot of 
p on t, are given in Fig. 43, AB for 3 cu. ft., GH for 24 cu. ft. The 
straight line EF represents the ideal line of pressure variation, related 
to AB, which would be traced if the law pv = RT were in control. The 
saturation line SS is not only the lower limit of a set of curves like BA, 
but each of these curves simply turns a corner at its A point, and all 
run down together along the saturation curve. That is, if cooling at 
constant volume be carried into the region of wet steam, there will be 
an increasing proportion of condensation as the temperature falls, but 
the pressure (now independent of volume) will merely drop according 



§ 12 (to)] THE PRESSURE AND VOLUME OF STEAM. 



77 



to the saturation relation. A quantitative illustration of this pro- 
gressive condensation will be found in § 13 (m) and Fig. 48. 

The short plotted lines of points on Fig. 43 show the experiments 
of Linde and associates — see Note 4, page 616, Appendix — which 
are decidedly the best measurements of steam volume related to pressure 



600 




"0 50 P 100 Lb.Abs. 150 200 

Fig. 43. — Curves of Heating at Constant Volume, for Superheated Steam. 

that have as yet been made. In these, pressure and temperature were 
varied together, while volume was kept constant and weight of steam 
present was known. On these observations was based Linde's formula 
for the relation among p, v, and t, from which Eq. (62) as here evaluated 
departs by only a very small numerical difference. The purpose in 
plotting the experiments is to show how closely they agree in form with 
the curves got from the formula. It appears that the observations do 
not run far into the region of superheat, neither do they go to very 
high pressures. 



78 



PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 



(n) The Isothermal Curve. — In Fig. 44 the isothermal is plotted 
in two ways, on pressure p as base (vertical). The curves in group I 
show product pv, while those in group II show volume directly. The 
same letters are used on corresponding points of the two groups. The 
ideal product RT or ps' from Eq. (60) now becomes the curve AC, 
instead of the straight line DE on the temperature base of Fig. 40, and 
AB is the saturation line. The ideal isothermal pv' = C is represented 
by the vertical straight line CD; the actual isothermal BD is an arc 
of a parabola, as appears from the form of F p in Eq. (63). 



250 



200 




Fig. 44. -*- Isothermal Curves for Steam, Wet and Superheated. Group I, Plot of 

pv on p: Group II, Plot of v on p. 

In the group of simple volume curves, C'A' shows the ideal satura- 
tion volume s', B'A' the actual volume s: curve CD' is the ideal iso- 
thermal pv' = C, and B'D' is the actual isothermal. Note particularly 
that the complete isothermal for steam is made up of two distinct parts : 
first the constant-pressure isothermal of vaporization EB', then the 
curve B'D' for superheated steam, the two meeting in a sharp corner 
at B'. 

The three cases of constant-pressure, constant-volume, and con- 
stant-temperature change are properly considered here, as among the 
fundamental properties of steam. Other conditions of expansion, like 
the adiabatic, will be taken up after the thermal relations have been 
set forth. 



§ 13 (a)] 



THERMAL PROPERTIES OF STEAM. 



79 



§ 13. Thermal Properties of Steam 

(a) Specific Heat of Water. — As stated in § 11 (a), the first step 
in "making steam" is to raise the water to boiling point. The heat 



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600 






































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500 










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II 

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ZOO B.T.U 400 600 800 1000 1200 

Fig. 45. — Heat Curves for Saturated Steam. 

Vertical base, temperature fahrenheit; horizontal ordinates in B.t.u. except 
for curve A. 

Curve A, specific heat c of water, given in col. 6 of Table III; scale marked 
along curve: § 13 (a). 

Curve BB, heat of the liquid q\ straight line BB' shows what q would be if c 
were constant at unity: § 13 (6), (e). 

Curve DD, total heat H; q and H meet at the critical point C: § 13 (c), (e). 

Curve EE, latent heat r, also shown by the intercept between BB and DD: 
§ 13 (c), (e). 



80 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. Ill 

required depends upon the specific heat of water, which varies accord- 
ing to the curve marked A on Fig. 45. From about 110 deg. fahr. up to 
about 530 deg., this curve has an equation of the form 

c = a-bt + dt 2 , ........ (69) 

a, b, and d being constant coefficients. Below 110 deg. the curve is a 
plot of experiment, not formulized; above 530 deg., the specific heat c 
gradually departs from this second-degree equation, in the direction of 
more rapid increase. The mean value of c from 32 deg. to 212 deg. is 
1.00, meeting the definition of the British thermal unit in § 5 (6), ac- 
cording to which it takes exactly 180 B.t.u. to raise one pound of 
water through these 180 degrees. This is called the mean thermal 
unit; from curve A it appears that the actual or local value of c is 
unity at about 50 deg. and again at about 153 deg. fahr. 

Numerical values of the specific heat of water are given in col. 6 
of Table III. 

(b) Heat of the Liquid. — In col. 6 of Table II is given the value of 
q, the heat required to raise one pound of water from 32 deg. to the tem- 
perature t in col. 0. It is derived, of course, by means of the relation 

q = J cdt (70) 

If the specific heat of water were constant at unity, q would be the same 
as (t — 32) ; actually, it differs from this number by an amount which, 
above 212 deg., increases at a growing rate. At 400 deg., for instance, 
(t — 32) is 368 and q is 373.9, an excess of 5.9 B.t.u. over the number 
of degrees of rise. 

Although the ice-melting temperature 32 deg. fahr. is naturally and 
properly taken as the starting point for measurement of heat of the liquid 
as given in the steam table, it is never the initial temperature for the 
operation of heating in the boiler. Instead, the feed water enters the 
boiler at some temperature U, and the heat required to raise it to the 
boiling point or vaporization temperature is (q — q ). 

(c) Heat of Vaporization and Total Heat. — The heat re- 
quired, at the boiling point t, to turn the pound of water into steam is 
called the heat of vaporization; its symbol is r, and it is given in col. 7 
of Table II. Since this heat all goes into the steam without causing any 
change of temperature, it is often called latent (hidden) heat. 

The sum of q and r, or the heat required for the whole operation of 
raising one pound of water from 32 deg .to t deg. and there completely 
evaporating it under constant pressure is called the total heat of sat- 
urated steam. The value of 

H=(q + r) (71) 

is given in col. 8 of Table II. 



§ 13 (d)] THERMAL PROPERTIES OF STEAM. 81 

(d) Partial Vaporization and Heat of Formation. — If the 
pound of water is not completely vaporized, the fraction x being changed 
into steam while (1 — x) or m remains as hot water, only the fraction x 
of the latent heat is taken up. For the general case of steam formation 
from water originally at U and with vaporization to the degree x, the 
heat absorbed per pound of water substance, called the "heat of forma- 
tion" of steam, is 

Q = (q - q°) + xr (72) 

It is often more convenient, as a method of calculation, to follow the 
formula 

Q = H - q - mr, (73) 

subtracting from the total heat, first the heat qo not required because it 
is already in the feed water, second the portion mr of the latent heat, 
not required because the m part of the pound of water remains un- 
evaporated. 

Using the word " steam" in a general way to cover the steam and 
water mixture (wet steam) which usually leaves the boiler and is de- 
livered to and works within the engine, we call the fraction x the "qual- 
ity" of the steam. Steam with 2 per cent of moisture (m = 0.02) has 
a quality of 0.98, or is 98 per cent dry. 

Example 5. — SteamJs made at a pressure of 120 lb. absolute from water 
at 142 deg., and leaves the boiler with 1.5 per cent of moisture. Find 

(a) Heat to raise water to boiling point. 

(b) Heat for vaporization. 

(c) Heat of formation. 

For v = 120, t = 341.3 (Table I). From Table II, for t = 341.3, q = 312.2; 
at 142 deg., q = 109.8; then 

( a ) q -q = 312.1 - 109.8 = 202.4 B.t.u. 

The value of r at 341.3 deg. is 877.6; the moisture effect mr is therefore 0.015 
X 877.6 = 13.2 B.t.u. Thus to compute mr and then subtract it is usually 
easier than to multiply r by x, and gives here 

(b) xr = 877.6 - 13.2 = 864.4, 

as the heat required for the actual amount of vaporization. 
Now the total heat requirement is 

(c) Q = {q - q ) + xr 
= 202.4 + 864.4 = 1066.8 B.t.u. 

Example 6. — In a boiler test the feed temperature was 185.6 deg., the steam 
pressure 113.6 lb. by gage, the quality of steam 0.982. Find (a) the heat that 



82 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 

would be required to make one pound of dry steam; (6) the heat of formation 
of the actual steam. 

V = H3.6 + 14.7 = 128.3 lb. absolute; t = 346.4 deg. 



Then 



q ■» 153.5 H = 1191.0 

r = 873.5 m = 0.018 mr = 15.7 

(a) Q' =H -q = 1191.0 - 153.5 = 1037.5 B.t.u. 

(b) Q = H -q -mr = 1037.5 - 15.7 = 1021.8 B.t.u. 



(e) Heat Curves. — On Fig. 45 are plotted the heat quantities 
just described, heat of the liquid q in curve B, total heat H in curve D 
These meet, in tangency, at the critical " point" C; at this temperature 
the liquid state vanishes, merging into the gaseous state without the 
intermediate stage of vaporization. Latent heat r is included between 
curves B and D, and is also laid out independently in curve E, from the 
zero line at the left edge of the diagram. Note that r is a decreasing 
function of t, and becomes zero at the critical temperature. The total 
heat increases to a maximum at about 490 deg. (see Table II), then 
decreases. The straight line B r shows how q would vary if the specific 
heat c were constant as 1.00. 

(/) External Work and Internal Energy. — During vaporiza- 
tion the volume change u — see § 12 (d) — is effected against the 
pressure p. This involves the performance of external work to the 
amount Pu or 144pw ft. lb., computed as in § 7 (d). Reduced to heat 

units this gives -i a a 

APu = ^—pu = 0.1851pw B.t.u (74) 

The external work thus done absorbs a portion of the heat of vaporiza- 
tion r, and the remainder 

I = r - APu (75) 

is what is expended in the disgregation work — see § 7 (a) — of chang- 
ing the substance from liquid to gas. This quantity I is called the inner 
latent heat of the steam. 

At the evaporation temperature t the pound of water has the volume 
w; and whatever work is required to bring it to this volume against the 
pressure p is here supposed to be included in the water heat q, so that 

k = q- APw (76) 

is the internal work of raising the temperature of the water. Then 

K = k + l = H-APs (77} 

is the total internal energy of the pound of dry steam. 

The external work quantities APw (for the water) and APu (for 
vaporization) are given in Table III, cols. 7 and 8, while the internal 



§ 13 (/)] THERMAL PROPERTIES OF STEAM. 83 

energies I and K have a more prominent place in cols. 9 and 10 of 
Table II. With this tabulation, the internal energy of one pound of 
steam in the condition defined by quality x or moisture m is to be found, 
not as 

I = k+xl, (78) 

but rather as 

I = K-ml (79) 

In the second expression we follow the analogy of Eq. (73); but 
internal energy / is always to be taken from the zero at melting point, so 
that there is no occasion for anything like the subtraction of g in Eq. 
(73). 

Example 7. — At a certain stage in the process within an engine, steam at 
the pressure 56 lb. has the quality x = 0.72; what is its internal energy? 
Forp = 56 we enter Table II with t = 288.25, getting 

K = 1096.1 I = 838.8 

then 

/ = 1091.6 - (0.28 X 838.8) 
= 1091.6 - 234.9 = 861.2 B.t.u. 

(g) External Energy of the Water. — Presupposing an ex- 
pansion from zero volume under constant pressure, we may call the 
product Pv the total external energy of the substance. In the case of 
the water in a boiler (at steam temperature), this energy or work really 
comes from two sources. Letting w be the volume at feed temperature, 
Pw is the work done by the feed pump in forcing the water into the 
boiler; and only the expansion work P(w — w ) is truly done at the 
expense of heat supplied. Then in getting from our steam table the 
value of the heat of formation Q, we ought in strict accuracy to sub- 
tract the feed-pump work — or else the table should be so made out 
that q will be only the heat supplied after the water gets into the boiler. 

There are good reasons — from considerations of convenience in 
making some important thermodynamic calculations, to be explained 
presently — why it is better to have H or Q include the total external 
energy APv. The actual value of APw is very small, not reaching 
one B.t.u. at the upper limit of the usual range of boiler pressures — 
see Example 8. This discrepancy is far within the probable error of 
any boiler or engine test, and is quite a little. less than the possible 
inaccuracy of the laboratory experiments upon which are based the 
values of q and r at high pressures. For these reasons we shall follow 
Examples 5 and 6 in the not quite theoretically correct practice of 
taking the tabular q to be the heat supplied within the boiler — when 
making calculations by Eqs. (71) to (73) for any ordinary conditions — 
•even though in perfect consistency it must be considered as including 



84 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 

also the work of the feed pump. In the table the latter assumption 
is followed, in that K is got from H by the method of Eq. (77), or by 
the subtraction of the full APs. For example, at 400 deg. saturation, 
from Table III, APw + APu = APs = 0.86 + 84.65 = 85.51; from 
Table II, H - K = 1201.86 - 1116.35 = 85.51. 

Example 8. — If steam is made at a pressure of 300 lb. absolute, how great 
an error is involved in calculating the heat of formation Q as if the water heat 
q in the table did not include the work of the feed pump? 

The feed water may have a temperature anywhere from 100 deg. to 212 deg., 
or w may be from 0.0161 to 0.0168 cu. ft. Then APw or 0. 185 pw will be from 
0.89 to 0.92 B.t.u. Subtracting this from the heat to be supplied changes 
H from 1205.9 to 1205.0, and would change Q by the same amount. Generally, 
the error involved in using the tabular value directly would be insignificant in 
anything like a boiler test; but if the physical data for q ever become of sufficient 
accuracy to give a real meaning to the correction just indicated, it can easily 
be made. 

Comparing this feed-pump work of about 0.90 B.t.u. with APw = 1.05 
as got by interpolation in Table III, we see that 0.15 B.t.u. is the portion of 
the "total external energy" of the water which in this case really comes from 
the heat supplied. 

(h) Specific Heat of Superheated Steam. — In the production 
of superheated steam (as distinguished from its use), the fundamental 
operation is heating under constant pressure, from saturation tem- 
perature t s to some higher temperature t. Knowing the value of the 
specific heat c p (which is not a constant, as it is for a gas), we can get 
the heat h a to be added by the operation 

h a = f c p dt (80) 

The data are in such shape that summation by short finite intervals 
will take the place of true integration. If the mean specific heat over 
the range from t 3 to t is known, an equivalent calculation is 

h = c pm (t-t a ). ........ (81) 

The specific heat under constant pressure is diagrammed in Fig. 46, 
with c p as ordinate, on a temperature base. The principal curves, of 
the type marked PP, show c p at a particular pressure, varying with 
the temperature; these curves are, however, designated by the satura- 
tion temperature rather than by the pressure, because they are deter- 
mined by chosen, simple-number values of this initial temperature. 
In general, c p is high at the start (against the saturation line SS), drops 
off rapidly but at a decreasing rate, and after passing a minimum begins 
to rise slowly. The highest curve drawn, that for 550 deg. saturation or 



> 



§ 13 (h) 



THERMAL PROPERTIES OF STEAM. 



85 



for 1045 lb. pressure, barely reaches its minimum within the limits 
of this diagram. From one pressure to another, c p rises with the pres- 



1200 
0.55 




0.55 



0.45 

200 300 Deg. 400 faHR. 500 600 700 800 900 

Fig. 46. — The Specific Heat of Superheated Steam under Constant Pressure, c p . 

The small separate sections complete the main diagram at top, right, and left. 
Scale of c p is varied as convenient. Curves of the class PP show c p on t, for the 
pressure corresponding to the saturation temperature by which each curve is desig- 
nated. Curve SS is the saturation line, at which superheating begins, and its ordi- 
nate is the initial, high value of c p . 

sure: outside of the region near the saturation line, the ratio of c p to 
p is, roughly, almost constant. 

(i) The Total Heat of Superheated Steam. — To the total heat 
H of saturated steam add the superheat h s ; the result, 

h = H + h s , (82) 



I 



86 



PROPERTIES AND BEHAVIOR OF STEAM. 



[Chap. III. 



may properly be called the total heat of superheated steam. It is to 
be denned as the total amount of heat required to start with one pound 
of water at 32 deg., and turn it into steam at pressure p and (any) 
temperature t, the whole operation being carried out under pressure p. 
The same definition will do for H — see Art. (c) — but for saturated 
steam we may say " steam at pressure p or temperature t." 

This important heat quantity is very fully laid out in Table VII, 
for which Fig. 47 serves as an explanatory diagram. When h is thus 



300 



200 



100 



Lb. 
Abs 





I s \ 

V \ 


A 




/ 




l\\ 


1 


sX 

Xo \8 


\ \r 
\ A 

\io \o 


W \i9 


\o o 

\io ICO 



1150 



H 



200 BT.U. 1250 



1300 



1350 



Fig. 47. — The Total Heat of Superheated Steam. 






Vertical base, absolute pressure in pounds per square inch; horizontal ordinate, 
total heat in B.t.u. Curve SS is the saturation line, showing H from Table II, 
col. 8. Curves of the class TT are lines of equal temperature; PP is a line of 
equal superheat. This]diagram is identical in terms with Table VII. Note that H 
as marked at the base of the diagram corresponds with the general symbol h in 
the text. 

plotted on p, the important fact appears that the isothermal TT is 
nearly a straight line. Close to the saturation limit there is a con- 
siderable bending (corresponding to the high values of c p existing in 
that region as shown by Fig. 46); but away from saturation the iso- 
thermal straightens, and as the temperature rises the slant diminishes. 
This all meets the rational requirements of the situation, for as the steam 
gets farther away from saturation it should approach a perfect gas in 
behavior, and for a perfect gas the isothermal will be a vertical straight 
line in the scheme of Fig. 47. 

The curve PP on Fig. 47 represents a class of lines of equal superheat 
which are drawn on Table-diagram VII and designated by their degrees 



§ 13 (i)] THERMAL PROPERTIES OF STEAM. 87 

of superheat. They are convenient when the idea of amount of super- 
heat is more prominent than that of actual temperature. In any case, 
they present at once the connection between the two. 

(j) Internal Energy of Superheated Steam. — Instead of fol- 
lowing the analogy of H and h, we let / represent the internal energy 
of the pound of superheated steam. Very obviously, 

I = h- APv (83) 

Example 9. — For one pound of steam at 150 lb. absolute and at 550 deg., 
find superheat, total heat, and internal energy. 

For 150 lb. the saturation temperature is t 9 = 358.5 deg. 

The superheat in degrees is therefore (t — t s ) = 191.5 deg. 

From Table VII, the total heat h is 1298.5 B.t.u. 

From Table II, the total heat H is 1193.8 B.t.u. 

The superheat in thermal units is then ha = 104.7 B.t.u. 

For the volume v, 

at 358.5 deg. saturation s' = 3.248 

R/p X (t - t s ) = 0.003970 X 191.5 = 0.760 

so that ■ v' = 4.008 

At 150 lb. and 550 deg., f p f t = 1.214 X 0.0581 = 0.071 

and the volume is v = 3.937 

Now the total external work is 

APv = 0.185 X 150 X 3.937 = 109.3 B.t.u. 

Finally, by Eq. (83), the internal energy is 

/ = 1298.5 - 109.3 = 1189.2 B.t.u. 

(k) Specific Heat at Constant Volume. — For a perfect gas 
there are two simple relations between c p and c v , namely, 

c p — c v = const., — = const. 

With superheated steam, especially when near to saturation, neither 
of these statements is true; but following the method of § 7 (6), as repre- 
sented by the equation c v = c p — AR, and finding the value of the 
quantity which corresponds to AR in Eq. (22), we can readily derive 
c v from c p for steam at any particular condition. 

The rate of expansion, as worked out in Example 3, § 12 (j), is the 
volume increment of one pound of steam, in cubic feet per degree of 
temperature rise, under the pressure p. The accompanying rate of 
external work-performance, analogous to AR in Eqs. (21) and (22), is 
very evidently 

A d -¥ = Ap( d 4\ '• • (84) 



dt \dt/p 



88 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. Ill 

In the example just referred to, the pressure was 150 lb., and the rate 
of expansion was found to be 0.00521 cu. ft. per degree at saturation 
and 0.00460 cu. ft. at 500 deg. Using 0.185p for AP as heretofore, we 
multiply these values by 0.185 X 150 = 27.75, and get 0.145 and 0.128 
for the respective rates of- external work, expressed in B.t.u. instead 
of foot pounds — compare the constant AR = 0.0685 for air, in § 7 
(6). Interpolating in Fig. 46 for t s = 358.5 deg., we find that c p is about 
0.692 at saturation and about 0.494 at 500 deg. Then by subtraction, 

at saturation, c v = 0.692 - 0.145 = 0.547; 
at 500 deg., c, = 0.494 - 0.128 = 0.366. 

Note that these two values of c v are not on the same volume line; they 
give conditions on two volume lines, at the points where these cross the 
pressure line for 150 lb. 

There is no occasion for a general working out of c v and the drawing 
of a diagram like Fig. 46. To get the heat added in a heating at con- 
stant volume, all that need be done is to calculate the internal energy at 
the initial and at the final state and subtract the first from the second. 

Example 10. — If one pound of steam is confined in a space of 4 cu. ft. and 

raised.from 350 deg. to 700 deg., how much heat is imparted to it? 

By interpolation on the curve for 4 cu. ft. in Table VI, the pressures are 

found to be, 

at 350 deg., p x = 114.01b; 

at 700 deg., p 2 = 171.5 lb. 
Referring to Table VII, the total heats are, 

at 114.0 lb. and 350 deg., hi = 1202.4 B.t.u.; 
at 171.5 lb. and 700 deg., h 2 = 1371.4 B.t.u. 

Calculation of the external work as 0.185 pv gives, 

at 350 deg., AUi = 0.185 X 114.0 X 4 = 84.3 B.t.u.; 
at 700 deg., AU 2 = 0.185 X 171.5 X 4 = 126.8 B.t.u. 
Subtraction of this A U or APv from h gives / ; 

at 350 deg., h = 1202.4 - 84.3 = 1118.1 B.t.u.; 
at 700 deg., h = 1371.4 - 126.8 = 1244.6 B.t.u. 

The difference, I 2 — Ii = 126.5 B.t.u., is the quantity sought. 
The mean specific heat, over the 350 deg. of rise, is 

c vm = 126.5 4- 350 = 0.362. 

The same general method is equally applicable when the operation lies 
wholly or partly within the region of wet steam, or of partial condensation. 

(I) Entropy of Steam. — Entropy is a very useful quantity in 
thermodynamic calculations for steam. Corresponding to the heat 
quantities q, r, and H, we have the entropy values given in cols. 11, 12, 



§ 13 (I)] THERMAL PROPERTIES OF STEAM. 89 

and 13 of Table II. To get more convenient symbols, a is used for A T q , 
the entropy of the liquid, and b for N r , the entropy of vaporization; then 
N is the total entropy, the sum of a and b. The methods of calculating 

a = N q = / -£ = / ^r; (85) 

and, since r is imparted isothermally, 

b = N r = Y (86) 

In being superheated at constant pressure, the entropy acquired is 

n= f T Tcj r or f T Tc f dt (87) 

The second way of writing the expression indicates the useful method 
of computing the ratio c p /T and then integrating or summing this on 
a temperature base. Also, with short enough intervals, say of ten 
degrees, there is no appreciable error in the simple summing of An = 
Ah/T m ; that is, An is got by dividing the heat added by the mean 
absolute temperature during the interval. 

(m) The Entkopy Diagram. — The fundamental temperature- 
entropy curves are given in Fig. 48. For any pressure, AB represents 
the reception of the water heat q and BC the reception of the latent heat 
r, while CD shows superheating at constant pressure — the area under 
each line being, of course, equal to the heat transferred. In terms of 
the tabular quantities, length QB is a or N q , and length BC is b or N r , 
so that QC is N. For superheat conditions,' n a is added to this N, to 
get n as diagrammed in Table VIII. The constant-pressure curves here 
shown, with starting points at from 40 deg. to 550 deg. on the satura- 
tion line, were computed as the basis for that table, and the interme- 
diate curves were located by interpolation. Keep clearly in mind that 
these lines are determined by particular values of pressure p, even 
though they are marked with the corresponding values of temperature 
on the saturation line. 

The origin of entropy, at the left edge of Fig. 48, is determined by 
the thermal condition of water at 32 deg. fahr., the same zero being taken, 
of course, as for heat measurement. The curve ABK is not only a plot of 
entropy a, but is also a curve of operation; the saturation line SCK 
is, however, to be thought of as a locus of condition or line of relation, 
not generally representing an operation. The critical point at K corre- 
sponds to C in Fig. 45. On this thermal diagram, K does not appear 
to be so very far above the upper limit of our service tables, at 550 
deg. saturation; but in terms of pressure the distance is relatively much 
greater. 



90 



PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 



Of the three fundamental simple operations, heating under constant 
pressure is completely represented by the broken line AB - BC - CD, 

|000 Q Q5_ N _W_ _J«L_ _m 25 




0.2 Q4 0.6 0.8 1.0 AT 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 



Fig. 48. — The Temperature-entropy Diagram for Steam. 

Vertical base, temperature fahrenheit; horizontal ordinate, entropy above state 
of water at 32 deg. Line ABK shows operation of water heating, up to any point B; 
BC is the operation of vaporization, CD that of superheating at constant pressure. 
The saturation line SCK serves chiefly as a locus of C or as a boundary between 
wet and superheated steam. Curve GEF is a line of constant- volume heating. 

very distinctly divided into its several parts. The isothermal is identi- 
cal with BC, and extends into the region of superheat as CT. One 



-j 



§ 13 (m)] THERMAL PROPERTIES OF STEAM. 91 

line of constant volume is fully given in GE - EF : above E, points on 
this curve are found by combining readings from Tables VI and VIII, 
not by using c v in an expression analogous to Eq. (87). Inside of the 
saturation line, the volume can be kept constant with falling pressure 
only by a partial (and rapidly increasing) degree of condensation. 

Example 11. — Find points on the constant-volume line GEF in Fig. 48. 

As indicated, this line is drawn for v = 10 cu. ft. 

First, get the point J, on the evaporation line at 250 deg. The saturation 
volume is s = 13.81 cu. ft., so that for 10 cu. ft. the quality must be x = 10 
-j- 13.81 = 0.724. Entropy b has the value 1.331, and in evaporation to 
x = 0.724, LJ = 1.331 X 0.724 = 1.109 is added to a = 0.382 at L, giving 
1.491 as the complete ordinate RJ. 

The point H, where the line for v = 10 cu. ft. crosses the constant-pressure 
line from 300 deg. saturation, is readily found by referring to Table VI and noting 
that this intersection there comes at about 668 deg. When seeking a point on a 
constant-pressure line not drawn on Fig. 48, as that at 290 deg. saturation, for 
instance, we first look in Table VI, and find that t = 514 deg. for this pressure 
and 10 cu. ft.; and from the 290-deg. line in Table VIII we get n = 1.778 for 
t = 514, and thus have the two coordinates of a point on the curve EF, Fig. 48. 



§ 14. yarious Curves and Operations 

(a) The Thkee Primary Operations, those at constant pressure, 
at constant volume, and at constant temperature, have been fully dis- 
cussed in § 12 (j) to (n) and in § 13 (m). Adiabatic expansion, the curve 
of constant quality, and the equilateral hyperbola pv = C are consid- 
ered in the section which follows. The line of constant total heat, at 
first sight a simple curve of relation, is really so closely connected with the 
steam-jet cycle that the next chapter seems to be the more appropriate 
place for its presentation, in § 17 (6). 

(b) Adiabatic Expansion. — As has been pointed out in § 9 (c), 
an adiabatic operation takes place at constant entropy, or is isentropic: 
that there can be no change of entropy without transfer of heat has 
been further emphasized in § 10 (d). The vertical lines of constant 
entropy in Fig. 48 (inclined in Table VIII) are therefore lines of adiabatic 
operation, expansion or compression. Inside of the saturation limit — 
anywhere within the region ABKCS, Fig. 48, including points on the 
boundary lines — relations are determined by computation : in the 
superheat region, only graphical methods are really available. 

For a steam and water mixture, as at J, Fig. 48, the entropy is, in 
analogy to Eq. (72), 

n = a + xb = RL + LJ; (88) 



92 PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 

or, following the idea of Eq. (73), 

n = N - mb = RM - JM (89) 

Here n is used as a general symbol for total entropy of wet steam, and 
N for the particular, limiting condition of dry saturation, as in Table II. 
To establish the adiabatic relation between two states designated 
as 1 and 2, say at H and K on Fig. 49, it is necessary to satisfy the con- 
dition 

di + xibi = a 2 + x 2 b 2 , (90) 

Most frequently, x 2 is the unknown quantity, to be got, of course, by 
the calculation 

(ai -f- xibi) — a 2 _ AH — DE /g-^ 

X2 ~ b 2 ~ EG 

The alternate method, rather preferable for slide-rule work because the 
numbers to be handled are relatively smaller in most cases, is to get the 
moisture fraction m 2 = (1 — x 2 ), by the relation 

KG N 2 - rii / Q9 n 

m2= EG = — K~ ( } 

In § 7 (h) was stated the general principle that in adiabatic expan- 
sion the external work done just equals the loss of internal energy. 
Letting 1 designate the initial (high-pressure) state and 2 the final (low- 
pressure) state, and using Eq. (79) for the internal energy /, we have 

A U = I 1 - I 2 = (K x - rmh) - (K 2 - m 2 l 2 ). . . (93) 

Example 12. — Let a space of 4 cu. ft. be filled with steam 350 deg. or 134.5 
lb. which contains 2 per cent of moisture; if it be expanded adiabatically to 
212 deg. or 14.7 lb., what will be the final condition and the amount of 
external work done? 

The tabular quantities needed are, 

At 350 sat. At 212 sat. 

si = 3.345 s 2 = 26.78 

ai =0.5032 a 2 =0.3120 

6i = 1.0753 6 2 = 1.4439 

Ni = 1.5785 A r 2 = 1.7559 

h = 787.7 U = 896.9 

#! = 1108.6 K 2 = 1076.9 

The initial specific volume is 2 per cent less than s h or V\ = 3.345 — 0.067 
= 3.278 cu. ft.: the weight of steam involved is therefore 4 -~ 3.278 = 1.2203 
lb. 

The initial total entropy per pound is, 

rti = 1.5785 - (0.02 X 1.0753) 
= 1.5785 - 0.0215 = 1.5570. 



§ 14 (&)] 



VARIOUS CURVES AND OPERATIONS. 



93 



Now applying Eq. 



m 2 = 



(92), 
1.7559 - 1.5570 



0.1989 



= 0.13774. 



1.4439 1.4439 

The dry-steam volume 26.78 is therefore diminished by 13.77 per cent of itself, 
or by 3.68, to 23.10 cu. ft. For the whole weight of steam present, the final 
volume is 23.10 X 1.2203 = 28.19 cu. ft. 

For h we have 1108.6 - (0.02 X 787.7) = 1108.6 - 15.8 = 1092.8; for 
I h 1076.9 - (0.1377 X 896.9) = 1076.9 - 123.5 = 953.4; then the external 
work is 1092.8 - 953.4 = 139.4 B.t.u. per pound of steam, or 139.4 X 1.2203 
= 170.1 B.t.u. total. 



AQO^ttA 




o 
o 
c> 


mom 
o o x o 


o 
o 


,c 


240 


/ / 


\ 


200 


/ / 


\ 


/ / 


\ 


160 


/ / 


\ 


A B 






\ 


120 

100 




J 




H \ 




J 










/ 










80 




/ 












1 










m m 




1 












1 










f 40 
Oeg. 30 




. 


































Fahr 




1 










LXJ 

15 

200 lo 

8 

pe 




j 








.. \^ 


D k 


/ 




K 




F \ G 




/ 












/ 












I 










La 4 

Abs. 3 
2 




j 












1 












I 












j 












1 




I 








Ql N 


/ 


T 


P 


r\ 


M \ s 


,00 O8 




/ 












1 










0.6 














0.4 




1 












1 










0.2 
0.1 




j 








> 




1 








\ 




i -I i i 
O- N C 


1 1 1 

.5 


• > 1 
1.0 


~\ — i — r 


1 i! 5 


.■■I. &> 



Fig. 49. — Change of Quality in Adiabatic Expansion. 
Same coordinates as in Fig. 48. Lines of class HP are adiabatics or isentropics; 
those of class HR are curves of constant quality or of constant steam weight. 

Example 13. — If one pound of steam at 150 lb. absolute (358.5 deg. sat.) 
and at 500 deg. fahr. is expanded adiabatically to 60 lb. (292.7 deg. sat.), what 
is its final temperature and what its initial and final volumes? 

The initial volume has been found in Example 2, page 74, to be 3.714 cu. ft. 

In Table VIII the initial entropy is read as 1.660; this would cross a line for 
292.7 deg. sat. at about 316 deg., which is therefore the final temperature sought. 

From Table VI the corresponding volume is found to be about 7.43 cu. ft. 

(c) The Change in Quality or condition during adiabatic operation 
is best illustrated by the method of Fig. 49, which consists in drawing, 



94 



PROPERTIES AND BEHAVIOR OF STEAM. [Chap. III. 



on the TN diagram, curves of constant quality like HR. Each of 
these is for a certain value of x, or it divides all the b or N r lengths, 
such as BC and QS, in a constant ratio. If adiabatic expansion begins 
with dry steam as at C or with steam weight predominant as at H, 
there is condensation as the pressure drops, shown by the swing of the 
^-constant lines CS and HR from the adiabatic lines CM and HP 
toward the right: steam is condensed to supply heat for external work. 
Starting with hot water as at B or with predominant water weight as 
at J, there is evaporation during expansion: the lowering of temperature 
releases an increasing proportion of the water heat q, and what is not 
needed for external work evaporates water. With half steam and half 




1.00 



1.02 



1.04 



1.06 



Fig. 50. — Comparison of Adiabatic Curves. 

Vertical base, ratio v/Vh to a scale made uniform for the logarithm of this ratio; 
horizontal ordinate, relation between values of the pv ratios in Table 5. 

water at the start, the two tendencies (toward condensation and toward 
evaporation) are just about equalized, as is shown by the nearly vertical 
course of the curve for x = 0.5. 

(d) Form of the Adiabatic Curve. — It would greatly simplify 
some important calculations, to be described in the next chapter, if the 
adiabatic pressure-volume curve could be represented by an equation 
of the form pv n = C. The exact form of this curve can be found only 
by means of the method illustrated in Example 12. In Table 5 and 
in Fig. 50 are given the results of an investigation into this matter. 

Five curves are computed, for initial pressures p\ of the values 
240, 120, 60, 30, and 15 lb. absolute; the initial quality Xi is unity, or 
the steam is dry-saturated at the start. The pressure ratio p/pi, used 



§ 14 (d) 



VARIOUS CURVES AND OPERATIONS. 



95 



as argument in the table and marked at the left edge of the diagram, 
is the. independent variable. The five columns with pressure headings 
give the results of the main calculation: the last column is from Zeuner's 
equation for the adiabatic of saturated and wet steam, 

pv n = c, n = 1.035 + 0.1 Xi (94) 

For initial dry steam, n = 1.135. 



Table 5. Comparison of Adiabatic Curves. 

of the Product pv. 



Relative Values 



p 

pi 


240 


120 


Pi 

60 


30 


15 


Formula. 


0.9 


.9866 


.9868 


.9856 


.9862 


9872 


.9877 


0.8 


.9734 


.9723 


.9708 


.9719 


9739 


.9738 


0.7 


.9580 


.9566 


.9552 


.9564 


9582 


.9583 


0.6 


.9402 


.9387 


.9371 


.9392 


9418 


.9410 


0.5 


.9195 


.9175 


.9167 


.9185 


9220 


.9206 


0.4 


.8954 


.8928 


.8924 


.8950 


8990 


.8968 


0.3 


.8650 


.8627 


.8628 


.8660 


8708 


.8666 


0.2 


.8247 


.8223 


.8230 


.8276 


8336 


.8258 


0.1 


.7610 


.7600 


.7621 


.7681 


7755 


.7604 


i 


.7048 


.7050 


.7083 


.7153 


7233 


.7002 


i 

?0~ 


.6545 


.6555 


.6605 


.6686 




.6443 


1 

TO 


.6102 


.6120 


.6174 






.5938 


1 
T?0~ 


.5856 


.5890 


.5945 






.5658 


T 

340 


.5493 


.5524 


.5585 






.5209 



The quantity given in the table is the ratio of the changing product 
pv to the initial piVi; in each column we see how this product decreases 
as the steam expands. The relative trend of the curves can best be 
seen in Fig. 50, where the true adiabatics are compared with the curve 
pyi.135 _ q »phe vertical line at 1.00 represents this standard, and the 
broken curves show the departures of the true adiabatics. For ex- 
ample, at p/pi = 0.1 and in the 60-lb. column, pv = 0.7621, in terms 
of initial piVi as unity; in the formula column the value is 0.7604. The 
difference, 0.7621 - 0.7064 = +0.0017, is not laid off directly, but 
is first reduced to a fraction or percentage of the formula value; so 
that 0.0017 + 0.7604 = 0.0022 is the distance from the reference line 
to the point on the curve. 

As in a number of diagrams where pressure as base has been plotted 
on a uniform scale of saturation temperature, it is here desirable to 
crowd together the high-pressure values and spread out those at low 
pressures. This effect is obtained in simple fashion by laying off 
log(p/pi) on a uniform scale, which gives the vertical spacing in Fig. 50. 



96 



PROPERTIES AND BEHAVIOR OF STEAM. {Chap. III. 



The diagram makes it evident that the equation does not very 
effectively represent the true law, especially if the expansion be carried 
to low pressures. Writing it in the form 



! >r = ' ^ 



(95) 



shows that as n is larger, pv is less; conversely, a rapid decrease in pv 
calls for a high value of n, a slow decrease for a lower value The shape 
of the true curves in Fig. 50 indicates that n ought to grow less as the 
pressure falls: at first the true pv decreases a little more rapidly than 
that by formula, but after passing equality (parallelism on the diagram) 
it shows a continually less rapid rate of decrease. In Eq. (94), n is 
supposed to be fixed by initial x x . If it were made a function of x or 
of p, down the curve, the equation might be accommodated to the true 
law, but it would then be too complicated for convenient use. Except 
for approximations of comparatively short range, the simple formula 
is not reliable. 

That the true adiabatics are of very much the same form, and in 
practical agreement over a considerable range of initial pressure, is a 
fact of much significance, which will be used later — see § 16 (d) and (g). 




Cu. Ft. 

Fig. 51. - 
A. Constant quality. B. 



15 



5 V 10 

■ Adiabatie Curves for Wet Steam. 
Exact adiabatie. C. Adiabatie by Eq 



(94). 



(e) The Effect of Initial Condition upon the form of the adia- 
batie pressure- volume curve is shown by Fig. 51, which transfers to 
this plane of representation the indications of Fig. 49. The five sets 



§ 14 (e)] VARIOUS CURVES AND OPERATIONS. 97 

of curves start at 160 lb. absolute, with x x equal respectively to 1.0, 0.75, 
0.5, 0.25, and 0.0; from each initial point is drawn the curve of constant 
quality, the true adiabatic, and (where distinguishable) the adiabatic 
by Eq. (94). The horizontal shading, emphasizing the departure of 
the adiabatics from constant quality, shows the condensation or evapo- 
ration that takes place. 

One thing made clearly evident by this diagram is, that as the 
initial proportion of water is greater, the ratio of expansion, or of v 
to the Vi at the start, is greater. The constant-quality lines are essen- 
tially alike in respect to this ratio. With high values of x h the adiabatic 
falls below the re-constant line; but as Xi grows smaller the adiabatic 
first rises to, then comes well above, the curve of constant quality. 
With hot water at the start, curve V, the- relative increase of volume 
is very much greater than in the case of curve I. 

The approximate Zeuner formula holds fairly well down to X\ = 0.7, 
but in the lower ranges of x± it entirely (and naturally) fails to represent 
the rapid increase in relative expansion just noted. 

The adiabatic of superheated steam conforms approximately to the 
equation pv n = C, with a value of n in the neighborhood of 1.3; but 
instead of attempting to apply this equation, with the necessary varia- 
tion in n, it is better to follow the method of Example 13, correlating 
temperature and pressure by the entropy relation, then going into 
Table VI or computing v from data in Table II. 

(/) The Curve of Constant Steam Weight. — On the pressure- 
volume diagram, the curve of constant quality, drawn as reference line 
in Fig. 51 and corresponding to HR in Fig. 49, is often called the curve 
of constant steam weight. If a mixture of steam and water expands 
in a cylinder without condensation or evaporation, the quality x re- 
maining unchanged, there is present a constant weight of steam (and 
of water). The saturation line B1-B2-B3 on Fig. 40 is one par- 
ticular case of this curve, for x = 1 ; the water-volume line B4 is another, 
for x = 0; and between these lie all possible values of x. The constant- 
weight curve is useful as a standard of comparison for the curves of the 
indicator diagram, measuring the condensation or evaporation during 
expansion and compression; further information concerning this matter 
will be found in §§ 22 and 23, and in § 27. 

(g) The Equilateral Hyperbola, pv = C, is much used in the 
analysis of indicator diagrams from the steam engine. The curve has 
no fundamental place in the theory of the engine, but it serves a useful 
purpose for two reasons. One is that the hyperbola is easier to lay out 
than the more logical curve of constant quality — see § 6 (g) and Fig. 29 : 
the other reason is, that as the result of the complex thermal reactions 



98 



PROPERTIES AND BEHAVIOR OF STEAM. IChap. III. 



within the cylinder the observed expansion curve generally approximates 
quite closely to the form pv = C, so that any marked departure from 
the hyperbola indicates something abnormal. 

The plot of pv on p in Fig. 52 is intended to illustrate and make 
quantitative the change in quality involved in expansion along the 
hyperbola. Any vertical line on the diagram represents the relation 
pv = C, and we need only compare these verticals with the XX curves 
of constant quality. Suppose, for instance, that in an engine the quality 
of the steam at cut-off is x\ = 0.74, the pressure being 100 lb. absolute; 



400 



?SO— i- 




C> 


' 


c> o 




o 




O UJ=3 

in D(^ 


8 






/ 




I 


-t 1 H - 


iii: 


,f 




/ 




/ 


200- \ 








_J 


-t t % - 


4 t 1 L 


7 


i 


r~ 




T/ 






/ 






JIT. 


•I 1 t^- 


/ 


/ 






/ 






/ 




/ 


4 t i - 


t 4 u i 


i 


/ 




/ 




150- 








/ 


t -i t i 


4 72P 


5 






/ 




— 


i 


r^ 




/ 1 


-44 t 


- t l 4- 




/ 


x 


/ 




- 


/ 






1 / 


--J- 4 4- 


--v -I 4- 




/ s 


-A2/ 






100— 


/ 






h 


-igt i i_ 


-4-JT t- 


7 




/ 




/' 


J 


/ 




1 

1 


I 


__/ r- £_ 


-fzt 4 - 


,'7 




/ 




/ 


p -- 


/ 




/ 




-4 4 -4 - 


-U t t< 


1 




/ 




/ 




1 




' 


! 


III: 


V -4-4 - 


/ 


/ 




/ 


/ 


*vO— -, 


1 


/ 




1 


-T ' t 4 


- J-l - 




/ 




/ 


rfo 


(o'i 




/ 




/ 


I 4 4 4- 


- PV t y 


/ 




^ 


/ 


UD._f 

Abs 




/ 




/ / 


- t 4-4-- 


-744 J- 




/ ■'*""' 


^7 




/ 


^n 


I 




,/ 


1 


—t WL- 


-t- t 7- 


s*f 




_i 






ou _ 


/ 




/ 




-4 4^-4 - 


/ -/ JL* 


'' 7_ 




/ 






*~ 


/ 




/ 




/+R // / /i 


- t 41 - 




/ 


' 


/ 


r~ 


20-= 


f 

i 


1 


/ 


> 


fT-Lzi 


-I4-4 _ 




/ 




/ 




- 


1 






/ i 


t t 7zz_ 


-t 7- 4> 




/ 


/ 


r 1 


/ 


:/ 




1 




/ / 


-JtJi-F* 


i -t 4- 




/ 


/ 




/ 


10- 


j 




/ 


/ 


// /A2/// 


- 7- 7- 


/ 




/ 












/ 


// 


-tfjTai 


i- -v J/ - 


/ 




/ 




/ 


- 


1 


, 


/ 


1' 


lJL iML. 


- Z Zt- 


/ 


/ 




/ 




5- 


I 


1 




Ml/ 


JTJAL-. 


_-/ _/!_ 


/ 




— <! 


/ 





300 



Dig. 
Sat 



200 



250 300 pv 350 



400 



450 



500 



550 



Fig. 52. — Diagram for the Equilateral Hyperbola. 



Vertical base, pressure on a scale uniform for saturation temperature; horizontal 
ordinate (along lines of constant pressure), value of the product pv. 

Vertical lines represent pv = C. 

Curves of class SS, XX, TT, lines of constant quality or of equal superheat, 
SS being the saturation line. 

Curves marked A, adiabatics. 



if the expansion curve conforms to pv = C, what will be the quality at 
release, this occurring at 25 lb. absolute? 

The initial state is first located, in the point C. Vertically below 
this, at 25 lb. pressure, is the point R. Reading its location between 
the XX lines for 0.8 and 0.85, we get x 2 = 0.814. The evaporation of 
moisture amounts, therefore, to 7.4 per cent of the total weight of steam 
and water in the cylinder. 






§ 14 (g)] VARIOUS CURVES AND OPERATIONS. 99 

In Fig. 52 are plotted also three of the adiabatics from Table 5, those 
with their saturation points at 240, 60, and 15 lb., in the curves Al, A2, 
and A3 ; and the last two are also extended into the region of superheat. 
It is of interest to note how near these come to being straight lines in the 
terms of this diagram, on what is really a base of saturation temperature : 
but in the absence of any workable relation between p and t, there does 
not appear to be any useful outcome in the way of a direct, simple rela- 
tion between pv and p. 



CHAPTER IV 
IDEAL STEAM CYCLES 

§ 15. The Static Pressure Cycle 

(a) The Carnot Cycle with Steam. — With the physical condi- 
tions described in § 8 (d) and with the same scheme of working, the Car- 
not cycle takes the form shown in Figs. 53 and 54 when steam is used as 
the medium. Starting at 1, there is in the cylinder one pound of water 

L 



100- 




120 La 341.3 Deg. 
IV II. 

in. 



15 LB. 213.0 Dec. 



I Lp. 101.8 Peg. 



N f.0 



B 



Fig. 53. — Pressure- volume Diagram 
for the Carnot Cycle. 



Fig. 54. — Temperature-entropy Dia- 
gram for the Carnot Cycle. 

These two diagrams are drawn for one pound of steam, and for the same govern- 
ing conditions; they give parallel illustration of the computations in Example 14. 



at temperature £1 and pressure pi; and isothermal expansion under con- 
stant pressure, to complete evaporation at 2, constitutes the first phase. 
Then follows adiabatic expansion to the lower limit of pressure and 
temperature at 3, completing the outstroke. On the return stroke 
there is first the isothermal compression 34, with condensation and rapid 
rejection of heat, then adiabatic compression along 41 to the initial 

state at 1. 

100 






§ 15 (a)] 



THE STATIC PRESSURE CYCLE. 



101 



As stated in § 8 (/) , the efficiency of this cycle is independent of the 
particular properties of the medium, provided only that the latter is 
capable of isothermal and adiabatic operations. Its value for steam 
as for a perfect gas, is therefore, 

1 1 — T 2 ti — t% 



E = 



T 1 



h + 459.6 



(96) 



the second expression indicating the more convenient method of cal- 
culation. Since the heat received during phase I is n, the useful work 
of the cycle, per pound of steam and expressed in heat units is 

AU = En . . . (97) 

The idea of this cycle will become more concrete, and the statement 
just made as to efficiency more convincing, by the working out of nu- 
merical values for a particular case. 

Example 14. — With the limiting conditions marked on Fig. 54, determine 
volume and heat values for the four points of the cycle, and work values for 
each phase and for the whole cycle. 

From Table II, by interpolation, 



Atp = 1001b., 



At v = 15 lb., 



t = 341.31 
s = 3.727 
q = 312.22 

r = 877.56 
H = 1189.79 



1 = 795.17 

K = 1107.00 

a = 0.49197 

b = 1.09573 

N = 1.58770 



t = 213.03 
s = 26.27 
q = 181.04 
r = 969.04 
H = 1150.08 



I = 896.15 

K = 1077.14 

a = 0.31353 

b = 1.44068 

N = 1.75421 



At point 1, forzi = 0.00, 

volume Vi =Wi = 0.018 cu. ft.; 
total heat hi = qi = 312.22 B.t.u.; 
inner heat /i = Ki - h = 311.83 B.t.u. 

At point 2, for a; 2 = 1.00, 

V2 = S2 = 3.727 cu. ft.; 
hi =H 2 = 1189.79 B.t.u.; 
I 2 =K 2 = 1107.00 B.t.u. 

At point 3, 



ra 3 = 



Nz - N 2 1.75421 - 1.58770 _ 0.16651 



= 0.11557; 



6 3 1.44068 1.44068 

v 3 = s 3 - mzsz = 26.27 - 3.04 = 23.23 cu. ft.; 
hi = Hz - rrizrz = 1150.08 - 0.1156 X 969.0 

= 1150.08 - 111.99 = 1038.09 B.t.u.; 
Iz=K 3 - mzU = 1077.14 - 0.1156 X 896.2 

= 1077.14 - 103.59 = 973.55 B.t.u. 



102 IDEAL STEAM CYCLES. [Chap. IV. 

At point 4, 

ai-a A 0.49197 - 0.31352 0.17845 niOQQA 

Xi = ~b7~ = I^oes = Ums = ai2386; 

y 4 = wi +XiU4= 0.017 + 0.1239 X 26.26 = 3.27 cu. ft.; 

hi = q* + z 4 r 4 = 181.04 + 120.02 = 301.06 B.t.u.; 

7 4 = (#4 - U) +x*U = 180.99 + 111.00 = 291.99 B.t.u. 
In phase I, 

heat imparted Qi = n = 877.56 B.t.u.; 

external work AUi = APxUi = r% — h 

= 877.56 - 795.17 = 82.39 B.t.u. 
In phase II, 

AUn =7 2 -h = 1107.00 - 973.55 = 133.45 B.t.u. 

In phase III, the length 34 represents (1 — m 3 — x 4 ) = 0.76057 of the total 
change from water to steam; then 

Qui = 0.76057 X r 3 = 0.76057 x 969.04 = 737.03 B.t.u.; 
AUm = 0.76057 X AP z u 3 = 0.76057 (r, - h) 
0.76057 X 72.89 = 55.44 B.t.u. 
In phase IV, 

AU iv =h -I* =311.83 -291.99 = 19.84 B.t.u. 

Now in terms of the phases, the total work in the outstroke is A(Ui+ Uu) 
= 82.39 + 133.45 = 215.84 B.t.u.; the negative work of the return stroke is 
A(*7m + Uiy) = 55.44 + 19.84 = 75.28 B.t.u.; and the net work is 215.84 
- 75.28 = 140.56 B.t.u. 

In terms of heat reception and rejection, the heat converted is Qi — Qui 
= 877.56-737.02=140.54 B.t.u., and the efficiency is 140.54 -v- 877.56 
= 0.16015. 

The initial absolute temperature is Ti = 341.3 + 459.6 = 800.9 deg., and 
the range of temperature 341.31 — 213.03 = 128.28; then the efficiency accord- 
ing to Eq. (96) is 

E = ^T = 0.16017. 
800.9 

To eliminate the small discrepancies which appear in the last figure of the 
results, it would be necessary to have tabular numbers carried to one more 
place — a degree of apparent accuracy entirely without physical foundation 
or meaning. As it is, the calculations above are carried one figure beyond 
what is of any practical significance. 



(6) The Availability of This Cycle, or its effective value for 
adaptation to actual conditions, is far higher with steam than with air 
as medium. In the example just computed, with a total piston dis- 
placement of V = V3 — vi = 23.21 cu. ft. (so that mean pressures are 
obtained through the division of foot-pound numbers by 144 X 23.21 
= 3342) , the work and pressure values which correspond to those com- 
puted in § 8 (h) are as follows : 









§ 15 (b)] THE STATIC PRESSURE CYCLE. 103 

Work Mean Pressure 

Forward stroke 215.84 B.t.u. = 167,920 ft. lb. 50.23 lb. per sq. in. 

Return stroke 75.28 B.t.u. = 58,570 ft. lb. 17.52 lb. per sq. in. 

Net or effective 140.56 B.t.u. = 109,350 ft. lb. 32.71 lb. per sq. in. 

Here the negative work drops into the position of relative insignificance 
which was occupied by the effective work in the previous case. This 
showing justifies the remarks made in § 8 (i) ; and we shall now proceed 
to consider the principal modifications which unavoidably accompany 
the actual embodiment of the idea of the Carnot cycle. 

Incidentally, it may be remarked that Fig. 54, besides giving a 
striking illustration of thermal efficiency in the ratio of area 1234 to 
area 12BA, suggests quite clearly the limits of possible steam-engine 
performance. The full-line rectangle represents the noncondensing 
engine, with moderately high boiler pressure. Lowering the exhaust 
pressure from 15 lb. to 1 lb. absolute — which can be done with a 
good condenser outfit, although 2 lb. is more usual — will raise the 
Carnot efficiency from 16 per cent to 30 per cent. If at the same time 
the initial temperature (of saturated steam) be raised to 400 deg., which 
is seldom exceeded in practice, the efficiency will be about 300 -s- 860 = 35 
per cent. A full consideration of engine performance forms the subject 
of Chapter VI. 

Note that in Fig. 54 the whole length of the absolute-temperature 
ordinates is shown. Generally, as in Figs. 48, 56, 58, etc., it is better 
to give only the useful range of temperature, to a much larger scale. 

(c) The Separation of Function. — In the wholly ideal Carnot 
engine, the entire cycle — namely, heat reception and expansion, heat 
rejection and compression — is supposed to be performed within the 
cylinder, using a confined and unchanged body of the working medium. 
While not absolutely impossible, this manner of operation is altogether 
impracticable, from considerations of convenience and of economy. 
The first step in the adaptation to actual conditions and materials is 
the separation of function, heat reception being assigned to the boiler, 
work performance to the engine, heat rejection to the condenser. We 
have to consider, then, the action of the whole steam plant, of which 
the engine proper is but one element. 

In the division of labor among the principal organs of the plant, 
phase IV of the Carnot cycle disappears. To realize it, we should have 
to withdraw from the condenser a proper mixture of water and steam, 
and let the feed pump compress it, in an approximately adiabatic 
fashion, to the pressure in the boiler. The possibility of such a process 
is very incomplete, and its attempted introduction would most unde- 
sirably increase the size, the power absorption, and the delicacy in 



104 



IDEAL STEAM CYCLES. 



[Chap. IV. 



action of the boiler-feeding apparatus. In the prevailing type of steam 
plant, the exhaust is all condensed (whether in a condenser or in the 
atmosphere), and the resulting water, or more commonly an equivalent 
amount of new water, is pumped into the boiler. 

The ideal cycle which really underlies the action of the steam plant 
is therefore not the Carnot cycle, but is what is generally called the 
Rankine cycle or the Clausius cycle. 

(d) The Rankine Cycle. — The diagrams in Figs. 55 and 56 repre- 
sent the following cycle of operations: 

(a) Feed water is pumped into the boiler at the exhaust temperature 
t 2 , against the full pressure p\, in Fig. 55, the work of the feed pump 
could be represented by a very narrow rectangle against the line OA; 
in Fig. 56, the line EA represents the operation of imparting the heat 
(<?i — #2), to raise the water from U to t\. 

(6) Isothermal evaporation begins at A, and as the steam is pushed 
up from the surface of the water it pushes out the layer ahead of it, 
and so there is a continued transmission of pressure work until the 
moving piston is reached, and the external work of vaporization is 
finally done upon that moving surface. The steam is supposed to 
flow along the pipe without loss of pressure or of heat; that is, the pipe 
is assumed to be frictionless and nonconducting. 

(c) The cylinder is taken to be perfectly nonconducting and non- 
absorbent of heat, as in the Carnot engine; then after steam is cut 




1 



Fig. 55. — Pressure- volume Diagram Fig. 56. — Temperature-entropy Dia- 
for the Rankine Cycle. gram for the Rankine Cycle. 

These diagrams are drawn with the same governing conditions as in Figs. 53 
and 54; computations in Example 15. 

off at B there is adiabatic expansion from B to C, carried clear down 
to the exhaust pressure. 

(d) From C to E is represented the outflow of the steam from the 
cylinder and its condensation, or, in Fig. 56, the abstraction of heat 
by the condenser. 



§ 15 (d)] THE STATIC PRESSURE CYCLE. 105 

The heat received, along EA and AB, is the total heat of formation 
above water at t 2 ; or, when the steam has entered the cylinder out to 
B, it carries the total heat hi. Leaving the cylinder, from C, it carries 
out the total heat h 2 corresponding to the condition of the steam at 
that point. The input of energy is therefore 

Qi= J hi-q 2 , (98) 

while the output of work is (hi — h 2 ) ; and the efficiency is given by the 
ratio 

E = hl ~ h2 (99) 

hi — q 2 

Here h is used as a general symbol for total heat above water at 32 deg., 
leaving H for the tabular value of 'the total heat of dry steam; and in 
what follows k will be used in the same manner in relation to K. 

Considering the work performance more in detail, we have in Fig. 55, 

work ABGO = AP iVi, 

work BCHG = I 1 -I 2 = ki- k 2 , by Eq. (93) ; 

work CEOH = AP 2 v 2 . 

Then the net work ABCE, in identity with the value above, is 
AU = APiVi + ki — AP 2 v 2 — k 2 
- =hi-h 2 (100) 

The use of the symbol hi instead of Hi for the total heat at B implies 
that the cycle is not limited to the case where the steam is dry-saturated 
at cut-off. In either of the cycles which have been discussed, there 
may be partial evaporation at this point; and the Rankine cycle is 
more general than the Carnot, in that it covers also the use of super- 
heated steam, since it does not require that the whole operation AB 
(Fig. 55) be isothermal, but merely that it be carried out under constant 
pressure. 

Example 15. — With the pressure limits pi = 120 lb. and p 2 = 15 lb. 
find the input, output, and efficiency of the Rankine cycle for three cases, 
namely, 

(a) With dry steam or complete evaporation at full admission, point B, 
Fig. 55 or Fig. 56; 

(b) For steam with 10 per cent of moisture; 

(c) For steam superheated to 500 deg. fahr. 

Cases (b) and (c) are represented by the dotted lines at the right-hand end 
of the diagram in Fig. 56. 

All the tabular values needed for this problem are collected in Example 14, 
and for case (a) the important quantities here required have been worked out; 
the changes in point designation are indicated in the tabulation below by 
bracketing the symbols used in Example 14. 



106 



IDEAL STEAM CYCLES. 



[Chap. IV. 



For case (b), with entropy b x equal to 1.0957, the presence of 10 per cent 
of moisture will diminish the total entropy, out to the adiabatic line, by 0.1096; 
and with b 2 = 1.4407 this will increase m 2 by the amount 0.1096 -r- 1.4407 
= 0.0761, making it 0.1156 + 0.0761 = 0.1917. The change in total heat hi 
will be 0.1 X 877.6 = 87.8, and that in h 2 will be 0.0761 X 969.0 = 73.7: the 
table contains the resulting quantities. 

For case (c), from Table VII total heat h = 1275.7, and from Table VIII 
entropy n x = 1.686; this exceeds the saturation value 1.588 by 0.098. At the 
lower pressure, 0.098 in 1.441 decreases m 2 by 0.068, making it 0.048, and in- 
creases h 2 by 0.068 X 969.0 = 65.9; these changes taking place from the 
values in case (a). 

The results are tabulated in condensed form. As compared with Example 
14, case (a) shows a drop in efficiency from 0.1602 to 0.1538. With the rec- 
tangular temperature-entropy diagram in Fig. 54, cutting off a piece at the right 
end (because of incomplete vaporization) would not change the efficiency; 
here it is lowered by the amount shown in case (6). In case (c) there is some 
rise in efficiency as compared with case (a), but because the increase in tempera- 



Case (a) 
mi = 


Case (b) 
mi= 0.10 


Case (c) 
h = 500° 


hi = im.8(h 2 ) 

h 1 -q 2 = l00S.S 
m 2 = 0.1156 (ra 3 ) 

h 2 = 1038.1 (h s ) 
h-h 2 = 151.7 

# = 0.1538 


1102.0 
921.0 

0.1917 
964.4 
137.6 

0.1494 


1275.7 
1094.7 

0.048 
1104.0 

171.7 
0.1568 



ture range (through extension above the line AB, Fig. 56) affects only a small 
portion of the heat handled, the change is not very great. 

(e) The Steam Engine Cycle. — Having passed from the Carnot 
to the Rankine cycle because of a fundamental change in the arrange- 
ment of apparatus, the next step to be made will cover the change from 
an ideal, thermally neutral cylinder to the actual, heat-absorbing and 
conducting metal cylinder. 

When the steam enters the cylinder it comes into contact with con- 
taining surfaces which have been cooled by exposure to the exhaust 
during the cycle just completed, and which have a high capacity for 
heat. During the admission period, then, a part of the steam is con- 
densed, its latent heat going into the metal of the cylinder and piston; 
it therefore shrinks in specific volume, one pound filling the space AB 
instead of AM in Fig. 57 (AM here is the same as AB in Fig. 55). With 
a given cylinder, this means that a greater weight of steam will be taken 
in during admission than would be needed if the steam remained in the 
state in which it comes from the boiler. 



§ 15 (e)] 



THE STATIC PRESSURE CYCLE. 



107 



The absorption of heat by the metal surfaces may continue into the 
first part of expansion; but as the pressure drops the temperature 
gradient soon reverses, and heat flows back into the steam, at an in- 
creasing rate. The result is, that instead of condensation to supply 
heat for external work, there is usually some reevaporation of moisture. 
Of the heat thus returned to the steam, a small (and as the temperature 
of return falls, a decreasing) portion is converted into work; but that 
which flows into, and is carried off by, the exhaust steam is altogether 
wasted. For this latter quantity, the action is equivalent to what was 
described in § 10 (h), inasmuch as it is a mere transfer of heat from source 
to receiver, without performance of any useful work. 

Because of the supply of heat which the steam receives from the 
cylinder as the pressure is lowered, the expansion curve usually approxi- 
mates quite fairly to the curve pv = C — this fact being wholly a matter 
of experience, not deducible by a priori reasoning. Of course, the exact 
form of the curve varies considerably with changing conditions, the 
study of which belongs to the next chapter. To get what we shall call 
the ideal steam diagram, we now assume that the equilateral hyperbola 
may be used as curve of expansion. 



BM 




1 

Fig. 57. — The Steam-engine Cycle, in Comparison with the Rankdne Cycle. 
See § 15 (e) and Example 16. 

(/) The Ideal Steam Diagram. — In Fig. 57, the effective initial 
volume AB is determined, from the full volume AM, by the percentage 
or fraction of initial condensation, for which ratio AM is the base. The 
curve BCH is of the form pv = C, according to the discussion in the 
last article. Expansion is not carried to the exhaust pressure at H, but 
is stopped at some earlier point C, and the line CD shows the operation 
of release. This is taken as equivalent to cooling at constant volume 
when laying out the temperature-entropy diagram, Fig. 58. The ex- 
haust, from D to E, is complete, or all the steam is expelled from the 
cylinder; in other words, the engine has no clearance space. In the 
present chapter we shall not go beyond this simple diagram. Its further 



108 IDEAL STEAM CYCLES. [Chap. IV. 

modification by secondary influences, such as pipe and valve losses (of 
pressure), clearance and compression, etc., will be taken up in the next 
chapter, with the study of actual indicator diagrams. 

(g) Incomplete Expansion. — There are two good reasons why it 
is advantageous to stop the expansion at C, Fig. 57, instead of carrying 
it to H. The size of an engine cylinder is determined by the necessity 
of its holding all the steam at the release volume OG. In comparing 
steam with air as a medium for use in the Carnot engine — see Art. (b) 
and § 8 (h) — the advantage of a high mean effective pressure and a 
small piston displacement has been well shown and strongly emphasized. 
With this idea in mind, it appears highly undesirable to make the 
cylinder volume, referred to the pound of steam, equal to OK instead 
of OG, merely to save the small work area CHD. 

Just what will be the best terminal pressure, at C, is a question to be 
settled by a judicious balancing of the evils of loss of available work on 
one hand and a needlessly big and costly engine on the other. The 
second reason for using incomplete expansion, now to be set forth, has 
a decided and definite influence in this connection. 

Suppose that all the frictional resistances in the machine are bunched 
together and reduced to an equivalent mean pressure on the piston, 
measured in the same terms as the steam pressure p — see § 28 (g) for 
some results from such a reduction. Let this be added to the back 
pressure OE, raising it say to OP. Then if the expansion be carried 
from G to K, the positive work of steam on piston will be CHKG, the 
negative work of piston on steam and against friction will be JCGK, 
and there will be a net loss equal to area JCH. It appears then that 
there is an actual loss of output in carrying expansion beyond the point 
where terminal pressure equals back pressure plus engine friction. This 
is the limit of economical expansion, and the considerations described 
in the first part of this article tend to keep actual working well within 
this limit. The terminal pressure varies with kind of engine and con- 
dition of service. In noncondensing engines it ranges from 25 to 40 lb. 
absolute, in condensing engines it is usually from 8 to 10 lb. These 
are normal values, for rated load; the pressure falls with underload, 
rises with overload. 

(h) The Tempekature-entropy Diagram for the steam-engine 
cycle is given in Fig. 58. Broken line EAM represents the combined 
operations of water heating and evaporation, in the boiler; MB shows 
the initial absorption of heat by the cylinder walls. Expansion line BC 
corresponds to the equilateral hyperbola in Fig. 57, and its slant toward 
the right is due to heat taken up from the metal surfaces, which in 
amount is equal to the area under BC, between vertical ordinates from 



§ 15 (h)] 



THE STATIC PRESSURE CYCLE. 



109 



B and C. In. general, the method of locating a point like R on the curve 
BC of Fig. 58 is to make the ratio QR/QS the same here as on Fig. 57. 
This can be done graphically, but measurement and slide rule computa- 
tion is generally less trouble than pure geometrical construction. Line 
CD represents cooling at constant volume (see Fig. 48), line DE plain 
condensation at constant pressure and temperature. The wasted work, 
or the portion of the ideally available energy which the engine fails to 
convert into work, is the area MBCDN. If we imagine the heat re- 
ceiver to be at the exhaust temperature t 2 , and assume that the waste 




Fig. 58. — Thermal -Diagram of the Steam-engine Cycle. Proportions 

correspond to Fig. 57. 

heat finally settles into the receiver at that temperature, it will increase 
the entropy acquired by the receiver from EN to ET — compare § 10 (c). 

(i) Work per Pound of Steam. — If we know the probable amount 
of initial condensation within the cylinder, and can thus fix the effective 
volume AB in Fig. 57, it is easy to calculate the work per pound of 
steam in the steam-engine cycle, for given pressure limits. The data are, 
boiler pressure pi, exhaust pressure po, and either the terminal pressure 
Pi or the ratio of expansion r = v 2 /vi. It is desirable to express the 
effective work in terms of pi, p , and v 2 . 

From Fig. 57 the component work quantities are : 



area ABFO = p&i = pi X v 2 X -', 

r 



area BCGF = pivi log e r = p\v 2 
area DEOG = p Q v 2 . 



log e r . 



Then the net work in foot pounds, with pressure values in pounds per 
square inch, is 

l+i^-po]. . . . 



U = 144 » 2 vi 



(101) 



110 IDEAL STEAM CYCLES. [Chap. IV 

The expression in brackets is the mean effective pressure of the diagram. 
Analyzed, it is the difference between the mean total pressure during 
the forward stroke, 

and the mean back pressure p m b or p in the return stroke. 

In designing an engine for a given power requirement, the first thing 
to do is to fix the size of the cylinder, and the first determinant called 
for is the mean effective pressure that can be expected. The simplest 
procedure is to compute a value with the help of Eq. (102), and modify 
it by an empirical " diagram factor" which takes account of the losses 
due to the secondary actions that have not yet been considered. Fur- 
ther development of this matter will be found in § 29 (6). 

Example 16. — In Fig. 57, p 1 = 120 lb., p 2 = 25 lb., p = 15 lb., x x = 0.75. 
Find work per pound of steam, mean effective pressure, and thermal efficiency. 
In Example 14, s x = 3.727; then v x here is 2.800 cu. ft., by Eq. (58). 
The ratio r is equally well got from pressures, or it is 120 -s- 25 = 4.8; there- 
fore log e r = 2.3026 log r = 2.3026 X 0.68124 = 1.5686; and 

1+loger = 2^686 = Q 53513 
r 4.8 

Now pmf = 120 X 0.5351 = 64.21 lb., 

and pm = 64.21 - 15 = 49.21 lb. per sq. in. 

Volume v 2 = 2.800 X 4.8 = 13.440 cu. ft. 

The effective work is 

U = 144 X 49.21 X 13.44 = 95,240 ft. lb. 
In heat units this is, 

AU = 95,240 -=- 778 = 122.4 B.t.u. 

The engine is supposed to have received dry steam, so that the problem is 
a continuation of case (a) in Example 15. There the heat supplied was found 
to be Qi = 1008.8 B.t.u., and the Rankine cycle efficiency was E\ = 0.1538 
— compare Eqs. (41) to (43), § 8 (g), for the different kinds of efficiency. 

Here then the absolute efficiency is 

E A = 122.4 -f- 1008.8 = 0.1213. 

The relative efficiency, which corresponds to area ABCDE -s- area AMNE 
in Fig. 58, is therefore 

For well-designed engines in good condition, the actual value ofr#R ranges 
from 0.6 to 0.7 — see Table 13, page 268. 

(j) The Regenerative Cycle. — A scheme for approximating 
the Carnot cycle in effect, used in some high-grade steam plants which 



§ 15 U)] 



THE STATIC PRESSURE CYCLE. 



Ill 








have to meet exceptional requirements as to thermal economy, is illus- 
trated in elementary fashion in Fig. 59. Going back to § 8 (c), and 
retaining the conditions of receiving all 
heat from without at T\ and rejecting 
all heat to without at T 2 , it must be 
remarked that the adiabatic is not the 
only possible process for the operations 
in which the temperature of the medium 
is raised and lowered. If in the tem- 
perature-lowering process some heat is 
abstracted and, without drop in tem- 
perature, carried over into the tempera- 
ture-raising process, less heat will be Fig. 59. - The Regenerative Cycle, 

rejected and less will have to be supplied. 

In its perfection, the scheme requires that the " expansion" (in the or- 
dinary steam-engine sense) follow on the temperature-entropy diagram 
the line BC, Fig. 59, exactly like DA; and the heat abstracted in this 
subadiabatic expansion is used to raise the feed water to the upper 
temperature t\. Actually, the heat abstraction takes place at several 
distinct points along the line of temperature drop, giving to the ideal 
operation (in a nonconducting engine) the stepped outline dotted on 
Fig. 59. This diagram corresponds to a quadruple-expansion engine, 
in which steam was withdrawn from each of the three receivers and 
from the low-pressure cylinder at release — see Fig. 140, § 27 (i). A 
series of feed-water heaters is provided, with pumps between them, and 
t the water is raised in pressure and temperature 

coincidently. 



fl 



§ 1 6. The Dynamic Force Cycle 



<F^ 



B P?[ 



H 



(a) The Steam Jet. — The conditions for the 
formation of a perfect steam jet are illustrated in 
Fig. 60. The large vessel A is filled with steam 
at the pressure p h which flows toward the outlet 
at a very low velocity V\. In entering and flow- 
ing through the nozzle B, the steam drops rapidly 
in pressure and gains in velocity; the work that 
would be done against the piston in an engine is here used in accelerating 
the steam itself, or is changed into kinetic energy of the jet. In the tube 
D the fully established jet has a high velocity 7 2 and throughout the 
steam substance there exists the stress or pressure p 2 - We assume that 
the material of the confining surfaces is thermally neutral, and that 



F 
Fig. 60. — Conditions 
of Jet Formation. 



112 



IDEAL STEAM CYCLES. 



[Chap. IV. 



these surfaces are frictionless. Under these assumptions, the expansion 
within the nozzle must be adiabatic and isentropic, for no heat can be 
received or lost, and there will be none of the throttling effect described 
in § 17 (d). 

(b) Enekgy of the Jet. — If the pressure or stress within the steam 
is plotted on instantaneous specific volume as base, the resulting dia- 
gram, Fig. 61, will be exactly like the Rankine cycle, Fig. 55. The 
amount of work done upon the steam mass and stored in kinetic form is 
determined by the following line of reasoning: 

As a pound of steam is pushed past any dividing plane like EF, 
Fig. 60, it receives the static-pressure work piVi from the steam behind 
it, and as it pushes past a dividing plane like GH it performs the work 
p 2 v 2 upon the steam ahead of it. In the drop from pi to p 2 it loses the 
internal energy (7i — I 2 ), which is equivalent to the area BCVG in 
Fig. 61. External work piVi plus internal energy l x is the total heat 
hi coming into the nozzle; external work p 2 v 2 plus internal energy I 2 
is the total heat h 2 going out of the nozzle; and since no energy is inter- 
changed with any outside body, the difference (hi — h 2 ) must be equal 
to the kinetic energy gained. Disregarding the approach velocity Vi, 
which is of insignificant value, and using plain V instead of V 2 , the equa- 
tion for the kinetic jet energy per pound of steam is 

E = ^ = 778 (hi - h 2 ) ft. lb (103) 



2g 



It is of interest to note that, whereas p dv is the element of static- 
pressure work (see Fig. 31), the corresponding element of jet energy 

is v dp, as indicated on Fig. 61. 
Briefly, suppose a slice of the nozzle 
space to be set off by means of a 
pair of cross planes exceedingly close 
together. At one plane the pressure 
is p, at the other (p — dp). The 
pound of steam having the volume 
v at pressure p, the unbalanced 
pressure dp acts through the vol- 
ume or displacement v, and does 

ilL, a? d 1 tv / the work v dp in producing the ac- 

.biG. bl. — Pressure-volume Diagram for / » 

t h e j e t. celeration dV/dt — this t being time, 

not temperature, 
(c) Cross Area of the Jet. — The method of calculating the 
energy E, Eq. (103), has been fully exemplified in § 15 (d). To get 
the velocity V at any condition p 2 , we need only make the calculation, 

V = V64.32x778(fti-/i2)= V50,040 (h-h 2 )= 223.7 Vhi-h 2 . (104) 










§ 16 (c)] THE DYNAMIC FORCE CYCLE. 113 

We shall take the unit jet to be that which discharges one pound of 
steam in one second of time. If we get the specific volume at p 2 , which 
will be V2 = X2S2, and note that this is in cubic feet while V is in feet per 
second, we find the cross area of the unit jet in square inches to be 

a =144^ (105) 

Example 17. — If steam initially dry at 120 lb. absolute expands in a 
perfect unit jet to 15 lb. absolute, what will be its energy, velocity, and area of 
cross section? 

In Example 15, case (a), for these data, hi and h 2 have been computed as 
1189.8 and 1038.1 B.t.u., respectively, and (hi - h 2 ) as 151.7 B.t.u. The 
kinetic energy is therefore 

E = 151.7 X 778 = 118,020 ft. lb. 

The velocity is 

V = V64.32 X 118,020 = 2755.2 ft. per second. 
With the final moisture-fraction m 2 = 0.1156, the volume v 2 is 26.27 — 3.04 
= 23.23 cu. ft., as in Example 14; then the area of the jet at 15 lb. pressure is 
found to be 

144 X 23.23 3345 



2755 2755 



= 1.214 sq. in. 



(d) Form of the Jet. — If, after the manner of Example 17 and 
with a given initial pressure p h the area a be computed for a series of 
values of the instantaneous lower pressure p, sl curve of area relative 
to pressure can be laid out, as in Fig. 62. Following the curve ABCDE, 
we see first a rapid decrease in area, shown by AB and due to the rapid 
growth of velocity. Presently, as the steam expands, specific volume 
gains on velocity, and the two keep well together through a long range 
of pressure, as is shown by the small variation in a from B to D. At 
the low-pressure end of the operation, volume grows much faster than 
velocity, hence the sharp rise in a along DE. At C the area has a 
minimum value, and this may well be called the throat of the jet; it is 
located at just 0.58 of the initial pressure. The fact that a jet of steam 
enlarges after it passes the throat pressure is the reason why an enlarg- 
ing or flaring nozzle must be used in order to get the full effect of a wide 
range of pressure drop. 

The limiting ordinates in Fig. 62, at the left for p = p h at the right 
for p = 0, are asymptotes to the a curve, calling for infinite values of a. 
The first condition implies zero velocity, which can never exist in a 
plant at work, because steam must flow, as from boiler to turbine or 
engine; still, steam-pipe velocities are so low compared with those in 
turbine jets that they correspond to points far up on the A end of the 
curve. At zero pressure, or for the ideal case of a jet flowing into a 



114 IDEAL STEAM CYCLES. [Chap. IV. 

perfect vacuum, while velocity would be finite, volume would be infinite, 
hence area would have to be infinite. In steam-turbine practice, a 
good working " vacuum" is in the neighborhood of 1 lb. per sq. in. 
absolute, and sometimes it even drops below 0.5 lb. 

In general form, the actual jet agrees with the ideal, but quantita- 
tively there is some discrepancy, due chiefly to failure to realize com- 
pletely the assumption that all the available heat energy is converted 
into kinetic energy of the jet. For the study and determination of the 
secondary, wasteful actions, it is necessary to compare the observed 
with the ideal jet; and after the degree of modification is known, it can 
be used to adjust values computed for ideal conditions. With these 
uses in view, it is important that the proportions of the ideal jet be in 
convenient shape for ready reference and comparison. 

(e) The Steam- jet Tables. — The proportions of the isentropic 
jet from initial dry steam are fully given in Table 6. As noted in the 
heading, this table represents exactly the jet which starts at 120 lb. 
absolute pressure. By means of the factors in Table 7, the numbers 
in Table 6 can be modified so as to fit jets from other initial pressures. 
The whole scheme is based on the assumption — a good approximation, 
although by no means rigorously exact — that in terms of pressure- 
ratio the jets are similar, in the geometrical sense of the word. The 
tabular quantities will now be defined and their use illustrated, and 
then the question of the real degree of similarity among jets from dif- 
ferent pressures will be more fully gone into. 

Pressure ratio p/p\\ This ratio of variant falling pressure to fixed 
initial pressure is the fundamental determinant, used as " argument" 
in Table 6 and as base in Figs. 62 to 65. The numbers in the other 
columns of Table 6 give the result of expansion from p x to p. 

Energy E and energy ratio Re: In col. 2 of Table 6, the jet energy 
in B.t.u. is the difference (^i — hi), as explained in Art. (b). For any 
other initial pressure than 120 lb., multiply this #120 by Re from Table 7, 
and the result will be E for the same ratio of expansion from the other 
pressure pi. 

Velocity V and velocity ratio Rv: In col. 3 of Table 6, the jet velocity 
in feet per second is derived from E by Eq. (104). For any other p h 
multiply this F120 by Rv from Table 7; note that Rv is simply the 
square root of Re- 

Volume ratio v/vi: In col. 4 of Table 6, this gives the exact form 
of the adiabatic curve from dry steam at 120 lb. initial pressure. How 
closely this column of ratios will fit curves from other pressures can 
be judged by reference to Fig. 50. 

Area ratio aja$: This shows the form of the jet, after the manner of 



§ 16 (e)] 



THE DYNAMIC FORCE CYCLE. 



115 



the curves in Fig. 62, but the measurement is made relative instead of 
absolute by giving any area a in terms of the throat area Oq. 

Area ratio R a and throat area a : R a is the ratio of the sizes of dif- 
ferent jets, showing how the jet from pi compares in cross area with 
that from 120 lb. It is got by dividing any Oo in col. 5 of Table 7 by 
the particular value 0.5868 for 120 lb. The two columns are strictly 
in parallel, Oo being the absolute value at the throat, in square inches 
for the pound-per-second jet, while R a shows relative values, not only 
at the throat but at any stage in the pressure drop. 



a 

Sq. 
In. 



1.0 



0.8 P/P. 0.6 



0.4 



t 
\ 
\ 

\ 

\ 
















— 1 — 
/ 
/ 

/ 

/ 


T-f- 
I l 

1 \ 


\ 


\ 
\ 
\ 












> 
/ 
/ 
/ 


j 


\ \ 

\\ 


\ 


\ 
\ 
\ 

\ 
\ 


s. 








S 


/ 
/ 
/ 


i 
i 


i 

> 1 


\ 
\ 
\ 
\ 




"■"v 

"-V^ 






iK___ 


—-""'' 


<5=p t 




i 
t 
i 
i 
/ 


i 
i 
/ 


A \ 


\ 














/ 


/ 
/ 


i 1 
/ /I 


1 \ 
1 \ 

\ \ 


s 












- — 


3Q.^- 


.'' 


/ 
/ 

/ 

s 


/ 1 
/ » 


\ \ 














60_ 


^' 




/ / 
/ / 

/ 


^_ 










C 




J20___ 




.*• 


/ 
















240= 


-P, 





0.2 



0.0 



Fig. 62. — Curves of Jet Area. 



Base, ratio of variant lower pressure to initial pressure; ordinate, cross area of 
ideal unit jet. Jets start from initial dry steam at the five (absolute) pressures 
marked on the curves. 

Napier divisor D and its ratio of variation, Rd : These are explained 
in Art. (h), where the help which D gives in smoothly interpolating oq 
and R a is also described. 

Example 18. — For an ideal jet from pi = 200 lb. to p 2 = 60 lb., find by 
means of the tables the final energy, velocity, and cross area. 

The pressure ratio p/pi is 0.3; for this datum we get from Table 6, 

E = 92.33, V = 2150, a = 1.224a . 
From Table 7, with p x = 200 lb., the energy ratio Re is 1.0240; this means 
that the energy of the 200-lb. jet is 2.4 per cent greater than that of the 120-lb. 
jet; the value is therefore, 

E = 92.33 X 1.0240 = 92.33 + 2.22 = 94.55 B.t.u. 



116 



IDEAL STEAM CYCLES. 



[Chap. IV. 



Table 6. Proportions of the Ideal Steam Jet 

Computed for initial dry saturated steam at 120 lb. per sq. in. absolute pressure. 



1 


2 


3 


4 


5 


l 


2 


3 


4 


5 


03 
0) 

u 
a . 

o <o 

•43 » 
o3 


o 

0) 

a 

m 


CO u 
• -■> <x> 

*« to 

'5 +» 


"o 

>*• 

.2 3 
+= 

a 

ft 


03 

a 
a) 

f-. 

03 

"8 

.2 

c3 


0) 

.9 3 

a 


gfpq 

a 
H 


-p" • 

o <D 

— <D 


"o 
> . 

o *> 

oS 
•43 =» 

K 


03 

03 
01 

u 

03 

'o 

.2 
%J 

03 


P. 

PI 


E 


• V 


V 


a 
a 


Pi 


E 


V 


V 


a 


0.00 


0.00 





1.000 




0.60 


40.80 


1429 


1.564 


1.0015 


0.99 


0.84 


205 


1.009 


4.512 


0.59 


42.09 


1451 


1.587 


1.0005 


0.98 


1.67 


289 


1.018 


3.221 


0.58 


43.40 


1474 


1.611 


1.000 


0.97 


2.51 


354 


1.027 


2.651 


0.57 


44.74 


1496 


1.636 


1.0002 


0.96 


3.36 


410 


1.037 


2.311 


0.56 


46.11 


1519 


1.662 


1.0007 


0.95 


4.22 


460 


1.046 


2.082 


0.55 


47.50 


1541 


1.689 


1.002 


0.94 


5.09 


505 


1.056 


1.913 


0.54 


48.91 


1564 


1.716 


1.003 


0.93 


5.96 


546 


1.066 


1.784 


0.53 


50.34 


1587 


1.744 


1.005 


0.92 


6.84 


585 


1.076 


1.682 


0.52 


51.80 


1610 


1.774 


1.008 


0.91 


7.73 


622 


1.086 


1.598 


0.51 


53.29 


1633 


1.804 


1.011 


0.90 


8.63 


657 


1.097 


1.527 


0.50 


54.80 


1656 


1.836 


1.014 


0.89 


9.54 


691 


1.107 


1.466 


0.49 


56.33 


1679 


1.869 


1.018 


0.88 


10.46 


724 


1.118 


1.414 


0.48 


57.88 


1702 


1.903 


1.023 


0.87 


11.39 


755 


1.129 


1.368 


0.47 


59.46 


1725 


1.938 


1.028 


0.86 


12.33 


785 


1.141 


1.328 


0.46 


61.07 


1748 


1.975 


1.034 


0.85 


13.28 


815 


1.153 


1.293 


0.45 


62.72 


1772 


2.014 


1.040 


0.84 


14.24 


844 


1.165 


1.262 


0.44 


64.40 


1795 


2.054 


1.047 


0.83 


15.21 


872 


1.177 


1.235 


0.43 


66.11 


1819 


2.096 


1.054 


0.82 


16.18 


900 


1.190 


1.210 


0.42 


67.86 


1843 


2.140 


1.062 


0.81 


17.17 


927 


1.203 


1.187 


0.41 


69.65 


1867 


2.186 


1.071 


0.80 


18.17 


953 


1.216 


1.166 


0.40 


71.48 


1891 


2.234 


1.080 


0.79 


19.18 


979 


1.229 


1.147 


0.39 


73.34 


1916 


2.284 


1.090 


0.78 


20.19 


1005 


1.243 


1.131 


0.38 


75.24 


1940 


2.337 


1.101 


G.77 


21.21 


1030 


1.257 


1.116 


0.37 


77.19 


1965 


2.392 


1.113 


0.76 


22.24 


1055 


1.271 


1.103 


0.36 


79.19 


1991 


2.450 


1.126 


0.75 


23.29 


1080 


1.286 


1.091 


0.35 


81.24 


2016 


2.511 


1.139 


0.74 


24.35 


1104 


1.301 


1.079 


0.34 


83.34 


2042 


2.576 


1.154 


0.73 


25.43 


1128 


1.317 


1.068 


0.33 


85.50 


2068 


2.644 


1.170 


0.72 


26.53 


1152 


1.333 


1.058 


0.32 


87.72 


2095 


2.717 


1.187 


0.71 


27.64 


1176 


1.350 


1.050 


0.31 


89.99 


2122 


2.795 


1.205 


0.70 


28.77 


1200 


1.367 


1.042 


0.30 


92.33 


2150 


2.877 


1.224 


0.69 


29.91 


1224 


1.384 


1.035 


0.29 


94.74 


2178 


2.964 


1.245 


0.68 


31.06 


1247 


1.402 


1.029 


0.28 


97.22 


2206 


3.057 


1.268 


0.67 


32.22 


1270 


1.420 


1.023 


0.27 


99.79 


2235 


3.156 


1.292 


0.66 


33.40 


1293 


1.439 


1.018 


0.26 


102.45 


2264 


3.263 


1.319 


0.65 


34.59 


1316 


1.458 


1.014 


0.25 


105.21 


2294 


3.378 


1.347 


0.64 


35.80 


1338 


1.478 


1.010 


0.24 


108.07 


2325 


3.502 


1.378 


0.63 


37.03 


1361 


1.499 


1.007 


0.23 


111.03 


2357 


3.636 


1.411 


0.62 


38.27 


1384 


1.520 


1.005 


0.22 


114.08 


2390 


3.781 


1.447 


0.61 


39.53 


1406 


1.542' 


1.003 


0.21 


117.27 


2423 


3.939 


1.487 



§ 16 (e) 



THE DYNAMIC FORCE CYCLE. 



117 



Table 6. Proportions of the Ideal Steam Jet — Continued. 



1 


2 


3 


4 


5 


l 


2 


3 


4 


5 


m 

■si 
.si 


.2, 

3 

c 


-1-3" . 

V 

>> 0) 

O <B 


> 

O 01 

oS 
"43 3 

03 
K 


m 

c3 
O 
u 
03 

*o 

.2 
o3 

(4 


to 
<D 

t- 
D. . 

•Sg 
.2 3 

03 


a 

*S 3 

£fPQ 


B 

H 




1 

> » 

.Si 

03 


m 

m 

c3 

"8 

'-3 

c3 


P 

Pi 


E 


V 


V 


a 


Pi 


E 


V 


Vl 


a 


0.20 


120.59 


2457 


4.113 


1.532 


0.04 


220.70 


3323 


17.21 


4.737 


019 


124.06 


2492 


4.305 


1.580 


0.035 


228.23 


3380 


19.40 


5.250 


0.18 


127.70 


2528 


4.516 


1.634 


0.03 


236.81 


3443 


22.33 


5.934 


0.17 


131.53 


2566 


4.749 


1.694 


0.025 


246.78 


3514 


26.23 


6.827 


0.16 


135.57 


2605 


5.010 


1.760 






















0.02 


258.66 


3598 


32.06 


8.15 


0.15 


13983 


2645 


5.305 


1.835 


0.018 


264.26 


3637 


35.28 


8.87 


0.14 


144.35 


2688 


5.639 


1.919 


0.016 


270.40 


3679 


39.17 


9.74 


0.13 


149.17 


2732 


6.023 


2.016 


0.014 


277.29 


3725 


44.21 


10.86 


0.12 


154.33 


2779 


6.469 


2.128 












0.11 


159.84 


2829 


6.988 


2.260 


0.012 


285.08 


3777 


50.81 


12.53 












0.010 


294.19 


3837 


59.69 


14.23 


0.10 


165.89 


2881 


7.60 


2.413 


0.008 


305.13 


3908 


75.40 


17.65 


0.09 


172.48 


2938 


8.35 


2.599 


0.006 


318.60 


3993 


95.16 


21.80 


0.08 


179.76 


2999 


9.27 


2.827 












0.07 


187.87 


3066 


10.43 


3.114 


0.004 


337.48 


4110 


137.9 


30.69 


0.06 


197.11 


3141 


11.97 


3.487 


0.003 


350.55 


4189 


178.9 


39.07 












0.002 


368.49 


4294 


258.9 


5515 


0.05 


207.84 


3225 


14.09 


3.999 


0.001 


396.71 


4456 


488.6 


100.29 


0.045 


213.85 


3271 


15.49 


4.331 













The velocity ratio being Rv = 1.0119, the new velocity is 
V = 2150 X 1.0119 = 2150 + 26 = 2176. 

The area a can be got in several ways. Using a/a Q = 1.224 from Table 6 
with tt = 0.3569 for 200 lb. from Table 7, we have 

a = 1.224 X 0.3569 = 0.4368 sq. in. 

Or, with a = 0.5868 and a/a = 1.224, the area of the 120-lb. jet at p/pi = 0.3 
is 

a 120 = 1.224 X 0.5868 = 0.7182 sq. in.; 

and with the ratio R a = 0.6081 for 200 lb. we have 

a = 0.6081 X 0.7182 = 0.4368 sq. in. 

Evidently, the first method is the simpler and more direct. 

The manner in which the computation of E and V has just been 
indicated shows the proper way to use the ratios from Table 7 with 



118 



IDEAL STEAM CYCLES. 



[Chap. IV. 



Table 7. Factoks for Different Initial Pressures 



1 


2 


3 


4 


5 


6 


7 


Initial pres- 


Ratio of 


Ratio of veloc- 


Ratio of cross 


Area at throat, 


Napier 


Ratio of varia- 


sure. 


energies. 


ities. 


areas. 


square inches. 


divisor. 


tion of D. 


pi 


Re 


Ry 


R a 


a o 


D 


R D 


250 


1.0326 


1.0162 


0.4892 


0.2871 


71.77 


1.0192 


240 


1.0311 


1.0154 


0.5091 


0.2988 


71.70 


1.0182 


230 


1.0295 


1.0146 


0.5307 


0.3114 


71.62 


1.0171 


220 


1.0278 


1.0138 


0.5542 


0.3252 


71.54 


1 . 0159 


210 


1.0260 


1.0129 


0.5799 


0.3403 


71.46 


1.0148 


200 


1.0240 


1.0119 


0.6081 


0.3569 


71.37 


1.0135 


190 


1.0217 


1 . 0108 


0.6392 


0.3752 


71.27 


1.0121 


180 


1.0192 


1.0096 


0.6738 


0.3954 


71.17 


1.0107 


170 


1.0166 


1.0083 


0.7123 


0.4180 


71.06 


1.0091 


160 


1.0138 


1.0069 


0.7556 


0.4434 


70.94 


1.0074 


150 


1.0108 


1.0054 


0.8046 


0.4721 


70.82 


1.0057 


140 


1.0075 


1.0037 


0.8605 


0.5049 


70.69 


1.0039 


130 


1.0039 


1.0019 


0.9250 


0.5428 


70.56 


1.0020 


120 


1.0000 


1.0000 


1.0000 


0.5868 


70.42 


1.0000 


110 


0.9956 


0.9978 


1.0882 


0.6386 


70.25 


0.9976 


100 


0.9904 


0.9952 


1.194 


0.7006 


70.06 


0.9949 


95 


0.9878 


0.9939 


1.255 


0.7364 


69.96 


0.9935 


90 


0.9850 


0.9925 


1.323 


0.7761 


69.85 


0.9919 


85 


0.9819 


0.9909 


1.398 


0.8205 


69.74 


0.9903 


80 


0.9786 


0.9892 


1.483 


0.8703 


69.62 


0.9886 


75 


0.9750 


0.9874 


1.579 


0.9265 


69.49 


0.9868 


70 


0.9712 


0.9855 


1.688 


0.9907 


69.35 


0.9848 


65 


0.9671 


0.9834 


1.814 


1.0645 


69.19 


0.9825 


60 


0.9627 


0.9812 


1.960 


1 . 1503 


69.02 


0.9801 


55 


0.9579 


0.9787 


2.134 


1.2525 


68.84 


0.9775 


50 


0.9526 


0.9760 


2.340 


1.3728 


68.64 


0.9747 


45 


0.9468 


0.9730 


2.591 


1.5204 


68.42 


0.9716 


40 


0.9401 


0.9696 


2.904 


1 . 7040 


68.16 


0.9680 


35 


0.9327 


0.9658 


3.304 


1.9390 


67.87 


0.9638 


30 


0.9242 


0.9613 


3.836 


2.2513 


67.54 


0.9591 


25 


0.9138 


0.9559 


4.579 


2.6868 


67.17 


0.9538 


20 


0.9008 


0.9491 


5.687 


3.3375 


66.75 


0.9478 


15 


0.8840 


0.9402 


7.523 


4.4147 


66.22 


0.9403 


10 


0.8610 


0.9279 


11.155 


6.546 


65.46 


0.9295 


5 


0.8275 


0.9097 


21.86 


12.827 


64.13 


0.9107 



the slide rule: that is, do not multiply the numbers from Table 6 by 
the whole ratio, but only by the difference between the ratio and unity; 
then add (or subtract) this result to get the adjusted value sought. 
(/) Similarity of Steam Jets. — The five curves drawn on Fig. 62 



§ 16 (/)] 



THE DYNAMIC FORCE CYCLE. 



119 



are intended to cover the whole range of common steam turbine practice. 
We shall now make a close comparison among these five jets, from initial 
dry steam at 240, 120, 60, 30, and 15 lb. absolute, with the especial pur- 
pose of testing the accuracy of the method of Tables 6 and 7. The 
quantities to be considered are, energy (which covers velocity), specific 
volume, and area; and of these, specific volume has been fully covered 
by § 14 (d), Table 5, and Fig. 50. 

In Fig. 63 the energy ratio Re is determined and interpolated. First 
of all, for each of the jets to be compared with that from 120 lb., there 

1.05 



1.00 



0.95 



Kx 



0.90 



0.85 



0.80 



^-^ 


240 










240 


120 




A 


B " 
A 


200 


160 




120 


H 


B 


""T~~~- 


90 


80 


70 


X 

60 


80 

\ 
\ 




60 




. **♦> 












50 \ 




















c 


40 


30 


30 


+ + 














\ 
\ 
\ 

\ 




20 








- 








\ 






I5 + 


B 


















B 

10 














o\ 






V 



Fig. 63. 



1.0 0.8 P/P t 0.6 0.4 0.2 0.0 

Comparison of Jet Energies, and Determination of Energy Ratio R E 



_ For lines AA and BB, same base as in Fig. 62; for curves BCD, ECF, base is 
initial pressure p\ (col. 1 of Table 7) to scales marked along curves. Ordinate is R E , 

was computed a series of values of this ratio. Thus at p/pi = 0.5, the 
energy of the 120-lb. jet is 54.80 B.t.u. (see Table 6), and that of the 
240-lb. jet is 56.44 B.t.u., both being calculated as indicated in Example 
17, but without reduction to foot pounds. Then Re = 56.44 -f- 54.80 
= 1.0299, and this value is plotted at the point H on Fig. 63. The 
short cross marks on the ordinate lines, keeping close to the BB lines, 
show the results of the calculations. These horizontal lines of mean 
ratio are drawn at the average height of the plotted points (except the 
rapidly rising points at the right-hand end of the lower curves). The 
departure of the points from the mean lines measures the error in the 






120 IDEAL STEAM CYCLES. [Chap. IV. 

assumption of a constant Re between the jet from pi lb. and that from 
120 lb., and in the use of Table 7. The small discrepancies between 
the plotted points and fair curves represent irregularities -in computation 
of the order of 0.01 to 0.03 B.t.u., and are due to the accumulation of 
fractional errors in the last figure of the steam table numbers. Dis- 
regarding these, we may say that the error in using a constant Re for 
the whole range of any jet does not exceed one-fourth of one per cent., 
except at the low-pressure end of the lower jets, where it rises to 0.5 per 
cent by the time a pressure of 1 lb. absolute is reached. 

The curves BCD and ECF, really the same curve to two scales, rep- 
resent Re as given in col. 2 of Table 7. After the BB lines had been 
fixed, the curve was drawn through the five points thus located, and the 
intermediate tabular values were measured from it. 

(g) Comparison of Jet Areas. — In Fig. 64, the group of curves 
near the line MN shows by how much the other four jets depart from 
similarity with that which begins at 120 lb. pressure. The comparison 
lies between computed and tabular values of the ratio a/a Q ; that is, 
between values computed for the other jets and those tabulated for the 
standard, 120-lb. jet. As an example, at p = 0.2 p h the area of the 
30-lb. jet was computed as 3.467 sq. in., while a for this jet is 2.251; 
then the ratio of jet proportion is a/a = 1.540. For the 120-lb. jet, 
the corresponding ratio is 1.532, by Table 6. If the jets were truly 
similar, these proportion factors would be equal; to show the degree of 
actual inequality, the ratio between them, 1.540 -f- 1.532 = 1.0052, is 
plotted in Fig. 64. From another point of view, it is as if the jet curves 
in Fig. 62 were brought together by means of factors — the factor a 
constant for any jet, and the reciprocal of R a in Table 7 — which 
would give them exactly the same ordinate at the throat, and ratios 
were then taken between the slightly differing ordinates at other points 
on the scale of pressure drop. 

In respect to form, as thus expressed in the manner of variation of 
cross area, the disagreement among the jets is far greater than in Fig. 63. 
Energy and velocity being so nearly in true similarity as is there shown, 
area will follow closely the trend of specific volume. Examination will 
show that the differences among the MN curves in Fig. 64 correspond 
almost exactly with those among the true adiabatics in Fig. 50, due 
account being taken of the different base scales in the two diagrams. 
Down to p/pi = 0.4, the jets conform within 0.25 per cent; but at the 
lower limit of 1 lb. absolute pressure (indicated by cross marks on the 
curves) the disagreement is from 1.0 to 1.7 per cent. 

(h) The Napier Divisor. — In order to fill out the columns for 
R a and ao in Table 7, it is best to interpolate first the Napier divisor 






§ 16 (h)] 



THE DYNAMIC FORCE CYCLE. 



121 



D. Napier's formula, long in use to calculate the flow of steam through 
an orifice, is 



/- 



70' 



(106) 



in which a is area of orifice in square inches, p is initial absolute pressure 
(our pi), and / is the weight of steam discharged per second. This 
formula holds if the low-side or terminal pressure pi is not greater than 
0.6 p\ — it may have any lower value That the pressure p 2 , provided 
only that it is below the throat pressure, has no appreciable effect upon 
the rate of flow is an important fact; it implies that the steam jet so 




P/P t 0.6 0.4 Q2 

Fig. 64. — Comparison of Jet Areas. 

Similar to Fig. 63 in general scheme. The curves on base MN, to scale at right, 
show departure of jets from true similarity: see § 16 (g). The curve ABC-EBF 
is the Napier divisor D, to the scale at the left, and with the scale of determining, 
initial pressure which is marked along the curve; see § 16 (h). 

adjusts itself as always to locate the throat of the jet in the smallest 
part of the orifice or nozzle. Whether or not the enlarging nozzle is 
present, to control expansion beyond the throat pressure, is a matter 
of very minor influence as regards rate of discharge. Further discussion 
of this question will be found in Chapter IX. 

Now putting our a for the a in Eq. (106), considering the unit jet 
so that / = 1, and using a general symbol D in place of the divisor 70, 
we get 

1= m, D = a oPl (107) 



122 IDEAL STEAM CYCLES. [Chap. IV. 

The variation of this D with p h for the ideal unit jet, is represented 
by the curve ABC-EBF in Fig. 64. This curve was laid out with a 
number of plotted points, more than those for the five jets in Fig. 62, 
and the tabular values were measured from it. Having D, division by 
pi gives oo, col. 5 of Table 7; and division of these numbers by 
the particular a Q for 120 lb., or by 0.5868, gives R a , which is the ratio 
of the absolute sizes of the jets. Finally, the degree of variation in the 
divisor D is shown by the ratio Rd, which is (D -f- D i2 o) Over the 
range of common boiler pressures D keeps close to 70, but for low initial 
pressures it falls off quite rapidly. 

Example 19. — With initial dry steam at 100 lb. absolute, compute the ideal 
flow through an orifice 0.5 in. in diameter, first, when the low-side pressure is 
80 lb. absolute; second, when it is 15 lb. absolute. 

The area of the orifice is 0.1964 sq. in., and we assume that it has a properly 
rounded approach or entrance. 

For 100 lb., throat area a is 0.7006 sq. in., by Table 7. For the pressure 
ratio 0.8, a/a is 1.166 by Table 6. Then the unit area in the first case is 

a = 0.7006 X 1.166 = 0.8169 sq. in. 

In general, the ideal rate of flow is equal to area of orifice divided by least 
area of unit jet. With discharge into 80 lb. pressure, the least area is that just 
computed, so that the rate of flow is 

/ = 0.1964 -r- 0.8169 = 0.24051b. per sec. 

With 15 lb., or with any other discharge pressure less than 0.58 p lf we use 
the throat area a ; then the flow in the second case is 

/ = 0.1964 -*- 0.7006 = 0.2803 lb. per sec. 

(i) The Effect of Initial Condition upon the form and dimen- 
sions of the ideal steam jet must now be considered. The comparison 
made in Fig. 65 covers this matter with sufficient completeness. For an 
initial pressure of 120 lb. absolute, the same as the "standard" in Tables 
6 and 7, jets have been computed for X\ = 0.9, 0.8, 0.7, and 0.0, and 
for initial superheats of 100, 200, 300, and 400 deg. The jet areas 
are laid out directly in the group of curves marked A, after the manner 
of Fig. 62, with the initial dry-steam curve emphasized. The three 
jets for high values of xi are very similar to that for X\ = 1.0, growing 
smaller in area with X\ at a slowly increasing rate; but the curve for 
all water at the start, or for x\ = 0.0, differs in having the throat or 
minimum area come much earlier on the pressure base, and then show- 
ing a much higher rate of enlargement. The only striking feature of 
the superheat curves is the general tendency to become relatively 
smaller, or to have a smaller rate of enlargement after passing the throat; 






§ 16 (i)] 



THE DYNAMIC FORCE CYCLE. 



123 



this is shown especially by their crowding against the dry-steam * curve 
at the low end of the pressure range. 

A much clearer showing of the relative sizes of the several jets is 
made in the B curves. At any pressure ratio, or on any ordinate line, 




1.0 0.8 P/P, 0.6 0.4 0.2 

Fig. 65. — Comparison of Jets with Different Initial Condition, All for 120 Lb. 

Initial Pressure. 

Curve groups A and B are on the base of pressure ratio; group A shows jet areas 
directly, group B relative areas. Curve C, on a base of quality x and superheat s, 
gives the Napier divisor D. 

the area ai. of the dry-steam curve is taken as base, and the quantity 
plotted is the ratio of the areas of the other jets to this standard. Here, 
then, we compare actual areas, as against the comparison of relative 
areas in Fig. 64, where each a was first referred to its own Oo, so as to 

* The word initial is understood; its omission, here and later in the discussion, 
need cause no confusion. 



124 IDEAL STEAM CYCLES. [Chap. IV. 

give the curves a common point at the throat of the jet. As an example 
of the present method, at p = 0.8 pi the area of the dry-steam jet is 
0.684 sq. in., from data in Table 6; the corresponding area of the 0.7 
jet is 0.577 sq. in.; and the ratio 0.577 -*- 0.684 = 0.844 is the ordinate 
of a point in the B curve for Xi = 0.7. 

It is now apparent that the wet-steam curves have a slight tendency 
to approach the " standard" as the pressure falls, or to become of the 
same absolute size, which tendency increases as x± is smaller, and be- 
comes stronger in the region of very low pressure. The superheat 
curves show the same tendency in much greater degree, and at low 
pressures they run into close agreement with the (initial) saturation 
curve, the line MN. The determination of the superheat curves, with 
data from Tables VI and VII, is necessarily less precise than the pure 
computations for adiabatics all in the region of saturated steam; con- 
sequently, with a possible error of perhaps one per cent in the " points" 
for these curves, too close inferences must not be drawn from the exact 
form of the B curves as here laid out. 

(j) The Principal Influence affecting the form of the jet, as 
measured by the instantaneous area a, is the varying specific volume 
v. Referring to Fig. 61, we note that if the expansion curve BC is some- 
what modified in form, so that v increases at a greater or less rate than 
in that diagram, there will be a slowly accumulating change in the value 
of area ABCD or energy E; but this change in E will be much less in 
proportion than the change in final v. The effect of variant initial 
condition upon the volume in adiabatic expansion has been brought' 
out in Fig. 51, and it will now be made clearer by a numerical com- 
parison. At a final pressure p 2 = 0.1 pi, the ratio of final volume v 2 
to initial volume Vi, for each of the eight closely grouped curves in 
Fig. 65 is as follows: 

Xi Si 



0.7 0.8 0.9 1.0 100 200 300 400 

vt/vi 8.08 7.88 7.73 7.60 6.87 6.30 5.89 5.70 

Here s is used as a symbol for superheat in degrees, not to be confused 
with specific saturation volume. For the one case not in this tabula- 
tion, that of Xi = 0.0, the corresponding ratio is about 240. 

A basis for the comparison of energy development is derived from 
the idea, made obvious by Fig. 61, that energy E is some function of 
the original product piVi; then a ratio of E to piv h or, in the present 
case of constant pi, of E to v h is a good measure of relative effect. One 
example will suffice: with p x = 120 and xi = 1.0, vi is 3.728 cu. ft.; and 
after expansion to 12 lb., E is 165.9 B.t.u. by Table 6; the ratio of 






§ 16 0)] THE DYNAMIC FORCE CYCLE. 125 

these numbers is 165.9 + 3.728 = 44.50. With xi = 0.7, Vi is 2.615, 
E is 120.1, and the ratio is 120.1 -f- 2.615 = 45.82. Now this ratio 
45.82 is only 3 per cent greater than 44.50, while the volume ratio 8.08 
is 6.3 per cent greater than 7.60, above. Since velocity varies as the 
square root of energy, so that the percentage of difference will be re- 
duced to 1.5 in this case, it appears that in a drop of xi from 1.0 to 0.7 
there is a relative increase in volume more than four times as great as 
the similar increase in velocity, and this accounts for the upward slant 
of the B curve for 0.7 in Fig. 65. With initial superheat, both volume 
and energy (referred to initial volume) fall off more rapidly than with 
saturated steam; but here again volume changes much the faster, hence 
the relative decrease in area of jet. 

(k) Flow of Steam. — To put this matter into definite shape for 
the particular initial pressure in Fig. 65, the least area Oo (which varies 
in position on the base scale according to the approximate locus TT) 
is measured and multiplied by pi or 120, after the manner of Eq. (107). 
The resulting values of" 2) are plotted in the curve CC, and from the 
smoothed curve Table 8 is obtained. In the second part of the table, 
the determinant is not degrees of initial superheat, as in the diagram, 
but the ratio of this superheat s or (t — t a ) to the absolute temperature 
T s = t s -\- 460 at saturation. 

Table 8. Napiek Divisor D, for pi = 120 Lb. absolute, Vary- 
ing with Initial Quality or Condition of the Steam 

in the Jet. 







For Wet Steam 








Quality X\ = 


0.7 


0.75 0.8 0.85 


0.9 


0.95 


1.0 


D 


59.6 


61.6 63.5 65.3 

For Superheated Steam 


67.1 


68.8 


70.4 


Ratio of superheat = 


0.0 


0.1 0.2 0.3 


0.4 


0.5 


0.6 


D 


70.4 


73.0 75.7 78.5 . 


81.5 


84.6 


87.9 



Now without undertaking the laborious task of making a number 
of comparisons like Fig. 65, we can get a working method for calculating 
flow of steam by assuming that the D curve for other initial pressures 
will be like that in Fig. 65, as set forth in Table 8. Then the ratio 
Rd in Table 7 can be used for adjusting values of D other than those 
belonging to the case of initial dry saturated steam. And even if the 
discharge pressure is higher than the throat pressure, at least a roughly 
approximate result can be got with the help of the ratio a/ao in the 
upper part of Table 6. The use of these methods, and the degree of 
error in their results, can best be shown by an example. 



126 IDEAL STEAM CYCLES. [Chap. IV. 

Example 20. — Find the ideal rate of flow per square inch of orifice in the 
following cases : 

(a) Pressure 60 lb. abs., quality 0.75, flow into atmosphere. 

(b) Pressure 200 lb. abs., superheat 320 deg., flow into 110 and into 160 lb. 
Case (a). Take from Table 8 the value D = 61.6, and to change from 120 lb. 

to 60 lb. multiply it by Rd = 0.980 from Table 7; then the new value of D 
will be 61.6 X 0.980 = 60.4. Dividing this by p x or 60, according to Eq. (107) 
we get a = 1.006; whence the flow per square inch is 1 -s- 1.006 = 0.994 lb. 
per second. 

Case (6). At 200 lb. pressure the saturation temperature is 382 deg. fahr. or 
842 deg. absolute; then the "ratio of superheat" is 320^-842 =0.380, for which 
D 120 is 80.9 by Table 8. The factor R D = 1.0135 from Table 7 changes this to 
D = 80.9 X 1.0135 = 82.0 for the jet from 200 lb. Division by 200 gives 
a = 0.410, which is the least area when the discharge pressure is 110 lb.; and 
for that condition the flow per square inch will be 1 -f- 0.410 = 2.44 lb. per sec. 

With p 2 = 160 lb. the pressure ratio is 0.8, and a/a from Table 6 is 1.166; 
this changes a to 1.166 X 0.410 = 0.478, and the rate of flow becomes 1 -s- 0.478 
=2.09 lb. per sec. 

To check the results in case (b), calculation by the "exact" method will now 
be made. At 200 lb. pressure and 320 deg. superheat, the temperature t is 
702 deg.; under these conditions the total heat hi is 1370.8 B.t.u. by Table VII, 
and the entropy m is 1.721 by Table VIII. Running down this- line of constant 
entropy we read t = 643 deg. at 160 lb. and t = 548 deg. at 110 lb. pressure, in 
Table VIII. For these pressures and temperatures, h 2 is read as 1344.0 and 
1300.5 B.t.u. The derived results are as follows: 

At 160 lb. 
discharge. 

Energy E= 26.8 

Velocity 7= 1155 

Specific volume, by Table VI, v= 4.07 

Area a = 0. 507 

By approximate method above, a= 0.478 

Per cent of error = 5.7 

It appears, then, that for a discharge determined by throat area the "approxi- 
mate" method is quite good; but for a higher discharge pressure it is so rough 
as to be of little use. The last conclusion is in full accord with the form of the 
B curves for high superheat in Fig. 65. 

(7) Flow of Water. — There is positively no use in carrying the 
comparison in Fig. 65 below X\ — 0.7, so far as steam and water mix- 
tures are concerned. But the extreme case of no steam at the start, 
or of the efflux of hot water, is of interest as underlying the actual flow 
of water through a boiler blow-off or try cock. Beneath the A curve 
for X\ = zero, in Fig. 65, is drawn the curve W, which shows to the 
same scale the ever-decreasing area of an ideal jet of cold water, driven 











At 110 lb. 




discharge. 




70.3 


B.t.u. 
ft. per sec. 


1870 


5.38 


cu. ft. 


0.415 


sq. in. 


0.410 


sq. in. 


1.2 


per cent. 






§ 16 (I)] THE DYNAMIC FORCE CYCLE. 127 

by the initial pressure 120 lb. The important facts brought out by 
the curve for hot water are: first, that only a small range of pressure 
drop (down to about 0.82pi in the figure) is available to drive the jet 
through the orifice; second, that even at this high throat pressure, the 
area is nearly four times that of the cold-water jet; in exact terms, this 
example shows the maximum ideal flow of hot water from 120 lb. as 
but 0.27 of the flow of cold water from 120 lb. to 98 lb. pressure. 
This marked effect of volume increase, due to the formation of steam 
within the jet, in cutting down the rate of discharge accounts for 
the lightness of the jet from a boiler blow-off, as compared with a 
jet of cold water from an equal orifice and driven by the same 
pressure. 

(m) Actual Flow of Steam. — The whole purpose of this section 
has been to put the ideal jet into shape for ready quantitative use. The 
essential requirement of the perfect jet is that all the convertible energy 
shall be put into the form of kinetic energy of the steam current. In 
the actual jet, this transformation fails of completeness in several 
directions. The closer study of these wastes is taken up in Chapter IX, 
as a preliminary to the analysis of steam action in the turbine; but a 
brief general description of them is appropriate here. 

With actual material for nozzle and other confining surfaces, there 
will be some loss of heat by conduction and radiation. Also, there is 
some tendency to abstract heat from the hot, high-pressure steam, 
conduct it along the nozzle, and give it back to the cool, low-pressure 
steam; but the possibility of such transfer action is absolutely insig- 
nificant when compared with its degree of prevalence in the piston 
engine. 

The nozzle surfaces offer a resistance to steam flow, of the general 
nature of friction. Mechanical energy thus absorbed goes back into 
the steam as heat, but under the penalty of only a small possibility of 
subsequent reconversion. 

Mechanical energy used to produce motions other than the direct 
forward flow of the current is wasted; anything that causes churning 
or whirling motion within the jet acts in this direction. Nonhomo- 
geneity of the substance, especially if it take the form of drops of water 
mixed with the steam at the start, greatly hinders proper jet formation; 
a drop of water will receive a much smaller acceleration, by a given 
unbalanced unit pressure, than will the same mass of steam, and each 
drop will serve as a center of eddying motion. All energy of secondary 
motion finally settles into heat in the steam at low temperature. 



128 



IDEAL STEAM CYCLES. 



[Chap. IV. 



§ 17. Throttling or Kinetic Pressure Lowering 

(a) The Action of Thkottling. — This name is given to the proc- 
ess through which the pressure of a current of steam is reduced from a 
higher value pi to a lower value p 2) by free or unresisted expansion. 
It occurs whenever steam flows through a partly opened valve or some 
other restricted portion of its channel, so that pressure work is used 
up in producing velocity and kinetic energy, but without any useful 
application of this energy. The term "wire drawing" is sometimes 
used as a synonym for throttling. 

This operation is so closely connected with jet formation, that we 
shall take the latter as a point of departure. Suppose steam to flow 



500 




Fahr. 



1.6 1.8 20 11 



Fig. 66. — Temperature-entropy Diagram, to Show Throttling Effect 
and Lines of Constant Total Heat. 

through an orifice or nozzle from pressure p\ to pressure p 2 . If the 
jet is perfectly formed, its kinetic energy will be equivalent to the area 
EABF on the temperature-entropy diagram, Fig. 66; the condition for 
"perfection" is truly adiabatic expansion from A to B. Now instead 
of using the steam jet to drive a turbine wheel or for some other effective 
purpose, let it simply come to rest in the low-pressure chamber, the 
kinetic energy being dissipated in whirls and eddies. The ultimate 
result is the reconversion of all the mechanical energy into heat; and 
as developed this heat comes back into the steam at p 2 until (if there 
has been no loss by radiation) the total heat has the same value as at 









§ 17 (a)] THROTTLING OR KINETIC PRESSURE LOWERING. 129 

A. In Fig. 66, the heating at constant pressure p^ is represented by 
BC out to the saturation line, then by CD in the region of superheat. 
The area under BCD, down to absolute zero, must equal area EABF. 
The point D lies on a line of constant total heat AD, drawn from A. 

(6) Constant Total Heat. — As already defined in several places, 
the total heat of steam is the amount of heat required to change water 
at 32 deg. into steam at a condition made definite by p, v, and t, the whole 
operation being carried out under the constant pressure p. For this 
general value the symbol h has been used, and it is the sum of the 
internal or intrinsic energy and of the external work or energy APv. 
In Fig. 66 the dotted curves are lines of constant total heat. For wet 
steam they are found from data in Table II, for superheated steam 
readings must be taken from Table VII. 

As regards the shape of these curves, it will be noted that in the 
region of wet steam they have the general trend of the saturation line, 
running nearly "parallel" to it at the top of the diagram, where the 
total heat H of dry steam is nearly constant, but bending toward it at 
an increasing rate as the pressure falls. With superheated steam, the 
curves show a rapidly dropping temperature at high pressure, but 
become nearly horizontal (isothermal) as the pressure approaches zero. 
This meets rational requirements, since steam approximates a perfect 
gas in behavior when pressure and density are low, and for such a gas 
the isothermal is the line of constant total heat. 

Example 21. — For the pressure 246.9 lb. (at 400 deg. saturation tempera- 
ture), determine points on the total heat curves for 1100 B.t.u. and 1260 B.t.u. 

From Table II, at 400 deg., H = 1201.9, r = 827.9; the total heat h = 1100 is 
101.9 B.t.u. short of complete evaporation, or m = 101.9 -^ 827.9 = 0.1230. 
The entropy b, length QR in Fig. 66, is 0.9631; then the distance from R to the 
1100 B.t.u. line is 0.1230 X 0.9631 = 0.1185 of entropy. 

For the other point sought, refer to Table VII. Run up the 1260 B.t.u. 
line to 246.9 lb. On this pressure line (horizontal), the distance between the 
490 deg. and 500 deg. isothermals is 5.5. B.t.u., while the 1260 line is 1.8 B.t.u. out 
from the 490 deg. line. To 490 deg. add 10 X 1.8 -^ 5.5 or 3.3, getting 493.3 
deg. as the temperature corresponding to 1260 B.t.u. By measuring this tem- 
perature up along the pressure line PR, the point where the constant-heat line 
crosses that curve is fixed. 

(c) Continuous Throttling. — In the operation represented by 
the outline AB-BCD, Fig. 66, jet formation or steam acceleration is 
distinct from and antecedent to the dissipation of kinetic energy, and 
the curve AD is merely a line of relation. This is an extreme and limit- 
ing case, never quite realized because perfect jet formation is impossible 



130 IDEAL STEAM CYCLES. [Chap. IV. 

under actual conditions. At the other extreme lies the operation of 
continuous or gradual throttling, which would be represented by the 
constant-heat curve AD. This is realized when steam is passed through 
a porous plug, or when a current of steam gradually falls in pressure in 
flowing along a nonconducting pipe. As fast as available energy is 
converted into the mechanical, kinetic form, it is changed back into 
heat through the overcoming of what we may call frictional resistances. 
If the process is truly continuous, the total heat in the steam will remain 
constant, and the drop from pi to pi will take place along the temperature- 
entropy line AD. 

Throttling, in the steam-power plant, usually occurs in such fashion 
that it would be represented by some curve intermediate between ABCD 
and AD : but no matter what is the detail of the process, the net effect 
is a change of state from point A to point D on the same total-heat line. 

(d) Increase of Entropy in Throttling. — In the operation of 
throttling, whether continuous or by parts, there is increase of entropy 
without reception of heat from any external source. At first sight, the 
process is adiabatic, and yet it is not isentropic. Any mental confusion 
over the matter will disappear, however, when it is remembered that 
the entropy held by a body is something which changes only when 
energy goes into or out of the substance in thermal form. In adiabatic 
expansion heat is changed into mechanical work, and its exit (from the 
store of heat) in this form does not affect the content of entropy; but 
when, in throttling, the mechanical energy of the steam current is 
changed back into heat and added to the store of heat, it brings entropy 
with it, just as if it were heat added from without to a quiescent body 
of steam. The process is adiabatic as regards the surroundings, but is 
not adiabatic as regards the steam itself. 

(e) Energy Transformed in Throttling. — In Fig. 66, area 
EABF represents the portion of the total heat (at A) that is changed 
into kinetic energy, and area under BCD shows the same energy as 
changed back to heat in the steam. For the case of continuous throttling, 
area EADCF, equal to area under AD, is the energy which goes through 
this double transformation. The difference is due to the fact that in 
the latter case heat is being continually returned to the steam, instead 
of being kept in the form of mechanical energy till the lower pressure 
is reached. The element of jet energy v dp in Fig. 61 becomes, in Fig. 66, 
a narrow strip GH or GKL, which can be expressed as n dt (with due 
regard to the proper method of measuring the n factor) : then with com- 
plete jet formation the energy given to the jet at p, and kept in it down 
to B, is the area of strip GH; in porous plug throttling the energy given 
and immediately returned is strip GKL. 



§ 17 (e)] THROTTLING OR KINETIC PRESSURE LOWERING. 131 

Fig. 67 shows the pressure-volume diagram corresponding to the 
part of Fig. 66 which illustrates our example of throttling. Develop- 
ment of the adiabatic jet, followed by dissipation of velocity at the lower 
pressure, is represented by the outline AB - BD, continuous throttling 
by the simple curve AD. The larger specific volume gained by keeping 
the total heat up to its full value, in the second case, is clearly shown, 
with the resulting increase of v dp from strip GH to strip GL. 




Fig. 67. — Pressure-volume Diagram for the Two Cases of Throttling Action. 

In final statement, the area ABCD in Fig. 66 or ABD in Fig. 67 is 
accounted for by saying that it represents energy which goes twice 
through the cyclical transformation from heat to work and back again, 
while EABF follows this cycle but once. 

(/) Reversibility of the Steam-jet Cycle. — In respect to the 
operations performed within the engine, the Rankine cycle, diagrammed 
in Figs. 55, 56, 61, and 66, is reversible. This is true whether work is 
done upon a piston or in accelerating the steam jet, provided only that 
the expansion with fall of pressure from pi to p 2 is isentropic. A swiftly 
flowing current of gas or liquid can, in a suitably formed retarding tube, 
be brought to rest with rise of pressure, and with the transformation of 
a large proportion of its kinetic energy into static-pressure work against 
the higher pressure. Ideally, if there were no dissipation of kinetic 
energy in secondary motions or in overcoming frictional resistances, 
the perfect steam jet would be completely reversible, and the steam 
could be driven right back into the chamber where the pressure pi exists. 

Examples of the reversed pressure-to-velocity cycle are found in the 
steam- jet blower and the centrifugal fan, the injector and the centrifugal 
pump. Complete reversibility, conditioned by equivalence between 
the kinetic energy of a jet and the static- pressure work which it can do 
in being brought to rest, is far from attainable. In general, the velocity- 
to-pressure cycle has a decidedly lower efficiency, actual and relative, 
than the direct or velocity-producing operation, accounted for by the 



132 IDEAL STEAM CYCLE. [Chap. IV. 

greater tendency to waste motion, with the ultimate conversion of useful 
energy into heat at low temperature. The same ideal of complete con- 
version of available energy underlies both actions, but in one direction 
the unavoidable wastes are greater than in the other. 

(g) Heat Waste in the Steam-jet Cycle. — The present chapter 
goes no farther than the formation of the jet, leaving for later discussion 
all questions as to the manner of harnessing it for useful output. In 
whatever way the jet is used, however, there will be some loss of ideal 
effect in its formation, and a further (and larger) loss in its application. 
The net result will be an increase of entropy from source to receiver, 
like that from N x to N 2 in Fig. 38 and from N to T in Fig. 58. Full 
throttling or complete dissipation of available energy, with reduction 
of the steam to the final state at D, Fig. 66, is an example of zero effi- 
ciency, of the same class as that in Fig. 39. In any working apparatus,, 
the energy waste will be of the order of magnitude shown in Fig. 38. 

It may be well to restate the fundamental fact that the rejection of 
the heat under line NE in Fig. 58 or line BF in Fig. 66 is absolutely 
unavoidable. The further rejection represented by area under TN in 
Fig. 58 is due to causes which, while they can never be eliminated, yet 
have their activity largely determined by the design and the manner 
of operation of the machine. 

- (h) Fall of Temperature in Throttling. — This has been shown 
in Fig. 66, and that it must always take place in the throttling of super- 
heated steam is indicated by the relation between the curves of constant 
total heat and of constant temperature in Table VII. The exact manner 
of this temperature change is shown in Fig. 68, in a direct plot of tem- 
perature on pressure, for which points are got from Table VII as in the 
latter part of Example 21. There are two groups of the constant heat 
curves HH. Those which have their origin (at the upper end) on the 
saturation line SS are determined by the initial pressure of saturation 
with which they are marked, and the value of the total heat along each 
can be found by reference to Table II. The upper curves do not touch 
the saturation line within the limits of this diagram (and above 1210 
B.t.u. are entirely clear of it): they are drawn for every 5 B.t.u., as 
indicated. 

In. connection with the lower set of curves in Fig. 68 are plotted three 
important sets of experiments upon the change of temperature in throt- 
tling. For any row of points there is a fixed initial pressure pi, and each 
point represents the temperature observed in an experiment made with 
a particular p 2 . The purpose in plotting the points here is to compare 
their trend with the curves derived from Table VII, which itself is 
largely based upon these experiments. The more irregular points are 



§ 17 (h)] THROTTLING OR KINETIC PRESSURE LOWERING. 133 

strung together by broken lines, merely to show that they belong to the 
same series. The apparatus used by the several experimenters, differing 



440 



20 P 40 60 80 \00 120 140 160 180 200 220 240 




Fig. 68. — Fall of Temperature in Throttling, or Curves of Constant Total Heat in 
a Plot of Temperature- £ on Pressure p. 

For references concerning the throttling experiments plotted, see Note 7, 
page 617, Appendix. 

quite widely in detail, was in every case a throttling calorimeter, made 
and operated with especial care. 

It is an important proposition in the physics of gases, that in con- 
stant-heat pressure lowering the rate of change of p with t is wholly a 
function of t; in other words, that curves like those in Fig. 68 should 
all have the same inclination at any particular horizontal line of equal 



134 



IDEAL STEAM CYCLE. 



[Chap. IV. 



temperature. For the purpose of testing the conformity of super- 
heated steam to this law, comparison is made between points Q and R 
in the figure. The line TT is drawn parallel to a tangent at Q on the 
curve for 1220 B.t.u.; and instead of being tangent at R is found to 
make a small angle with the curve for 1245 B.t.u. This discrepancy 
is due either to an as yet insufficiently accurate determination of the 
properties of steam, or possibly to a slight departure from the law in 
the region near to saturation. 

(i) The Throttling Calorimeter. — This instrument, based upon 
the fact that in throttling or free expansion there is no change of total 
heat (unless through escape in radiation), is used to find the quality 
of moist steam. As outlined in Fig. 69, steam is drawn from the steam 




Fig. 69. — Throttling Calorimeter. 

main S, through the perforated pipe P and open valve V, into the cham- 
ber C where, at pressure pi, the temperature h is read. It then flows 
through the small orifice into the low-pressure chamber L, open to 
the air, and the temperature after throttling is read as t 2 . Provided 
only that this t 2 is greater than t s2 (here 212 deg. ), the total heat is definite 
in terms of pressure and temperature; and being measured at p 2 is 
known in value for the steam as originally at p\. The actual total 
heat h 2 (equal to hi) can be read from Table VII for p 2 and t 2 ; then for 
the original deficiency in total heat due to incomplete evaporation, and 
for the fraction of initial moisture we have, 

H!-h 2 



m\f\ = Hi — h 



2, 



mi = 



n 



(108) 



Example 22. — In a throttling calorimeter which discharges into the atmos- 
phere, the temperature readings (corrected) are U = 334.5 deg., t 2 = 261.4 deg. 
What is the quality of the steam tested, assuming no radiation from the calo- 
rimeter? 



§ 17 (i)] THROTTLING OR KINETIC PRESSURE LOWERING. 135 

The pressure corresponding to 334.5 deg. is 109.5 lb. absolute or 94.8 lb. by- 
gage, the total heat of dry steam is Hi = 1188.1 B.t.u., and the latent heat r x 
is 883.0 B.t.u. At the pressure of the atmosphere and at 261.4 deg. the total heat 
h 2 , by interpolation between the isothermals for 260 and 270 deg. in Table 
VII, is 1173.4 B.t.u. This is also the actual total heat of steam at p x with 
moisture m x ; then the heat shortage is miri = 1188.1 — 1173.4 = 14.7 B.t.u., 
and the fraction of moisture is 

mi = 14.7 -?■ 883.0 = 0.0167, or 1.67 per cent. 

(j) Diagram for the Throttling Calorimeter. — To facilitate 
the calculation just illustrated, several important quantities are dia- 
grammed in Fig. 70, for the case of discharge into the atmosphere. The 



1210 




40 p, 60 80 Lb. I00abs.I20 



220 



Fig. 70. — Diagram for the Throttling Calorimeter. 

base is initial pressure p h with which is laid out a variable scale of 
corresponding saturation temperature t\. Curve A A shows, to the 
scale at the left, the temperature t 2 which results from the throttling of 
initially dry steam to atmospheric pressure, or to p 2 = 14.7 lb. absolute; 
note that while this is for p\ as scaled below, it is at p 2 . Curve BB is 
the total heat Hi of initially dry steam, existing also at p 2 as the value 
of h 2 correlative with the maximum t 2 given by curve AA; in the latter 
relation, h 2 on BB is directly under the corresponding t 2 on AA. To 
obviate the need of looking up ri in Table II, it is laid out in curve CC, 
from which it can be read with sufficient accuracy. If the existing 
pressure of the atmosphere is something other than 14.7 lb. or 29.92 in. 
of mercury, a correction must be made in the value of h 2 for t 2 . Refer- 
ence to Table-diagram VII shows that for a given temperature t the 
total heat h increases as pressure falls, decreases as it rises, so that the 



136 IDEAL STEAM CYCLE. [Chap. IV. 

rate of change is negative. The coefficient of variation, dh/dp (which 
changes with the slant of the isothermal lines in Table VII), is given by 
curve DD, for which the base is the scale of B.t.u. at the right; the 
rate is expressed in B.t.u. per pound of pressure. Finally, curve EE 
shows, for any p h the limiting or maximum value of moisture mi that 
can be measured by the calorimeter with discharge into the atmosphere ; 
this matter is explained in the next article. 

Example 23. — By means of Fig. 70, find indicated moisture from the 
following data: Temperatures, t x = 342.6 deg., t 2 = 242.7 deg.; barometer read- 
ing 29.3 in. mercury. 

For t x = 342.6, px reads about 122 lb. by the parallel scale of pressures 
(122.1 by table), and the total heat of dry steam, from curve BB above this 
pressure, is 1190.1 = Hi. With dry steam, from this pressure, the temperature 
after throttling would be 297.0 deg., as read from curve AA at the ordinate for 
Pi — 122. The difference between this and the actual t 2 = 242.7 is due to the 
initial wetness of the steam tested. 

Now locate the temperature 242.7 deg. on curve AA (as a vertical measure- 
ment, according to the scale at the left), and read beneath it on curve BB the 
value 1164.6 B.t.u. for h 2 . This must be corrected for the barometer reading; 
and since the latter is below normal, h 2 must be increased. The pressure p 2 
is 0.62 in. or 0.3 lb. low; from curve DD the coefficient of variation, at H = 1165 
is 0.31 B.t.u. per pound, so that h 2 must be increased by 0.3 X 0.31 = 0.09 or 
0.1 B.t.u., making it 1164.7. The heat shortage or moisture effect is now 

mxrx =Hx-h 2 = 1190.1 - 1164.7 = 25.4 B.t.u. 

From curve CC, n = 877, then m x = 25.4 •*■ 877 = 0.0290, or 2.9 per cent. 

In the use of this diagram, there is liability to an error of about 0.5 B.t.u. 
in rrtxTx, from purely graphical inaccuracy; but this is a good deal less than the 
possible experimental error. 

(k) Range of the Calorimeter. — As suggested in the example 
just worked, the effect of initial moisture is to lower the temperature t 2} 
diminishing the superheat of the discharged steam. Evidently, if the 
wetness at p\ exceeds a certain amount, i 2 will fall to 212 deg. (or to the 
saturation temperature at any p 2 ), and the final state of the steam will 
cease to be determinate with respect to total heat. Curve EE in Fig. 70 
shows the maximum measurable value of mi. To find this amount of 
moisture which will just lower t 2 to 212 deg., subtract from Hi the total 
heat H = 1149.7 at 212 deg., and divide this heat difference by r±. If, 
for instance, the existing total heat at 200 lb. pressure is 1149.7, the 
full heat being 1198.6, the shortage is 48.9 B.t.u.; and with the latent 
heat r\ = 843.8, the fraction of moisture is 0.0580. The last number 
gives a point on curve EE. 






§ 17 (/c)] THROTTLING OR KINETIC PRESSURE LOWERING. 



137 






In practice, it is not well to use the throttling calorimeter alone if 
t 2 falls below 220 deg., with atmospheric discharge. 

(I) The Separator Calorimeter. — With steam that is quite wet, 
a small separator, similar to those used in pipe lines for the purpose of 
removing water from the steam current, is a very 
effective quality meter. As outlined in Fig. 71, the 
separator is intended to be coupled in on the high- 
pressure side of the throttler in Fig. 69, at the union 
U, when the steam is too wet for the first instrument. 
This combination constitutes the older form of the 
Barrus Universal Calorimeter; the separator takes 
out nearly all of the moisture from the sample, send- 
ing almost dry steam over into the throttler. If the 
separator is to be used alone, there must be a throttle 
valve or a discharge orifice in its steam outlet. In 
any case, the drain valve D is so manipulated as to 
keep the water in the chamber C at or near a certain 

level (shown in the glass gage G), well below the Fig. 71. —Separator 
,, „ .. . . . . _. Calorimeter. 

mouth ot the inlet pipe r. 

If gi = weight of steam discharged in a certain time and g 2 = weight 

of water separated, so that g = gi -f g 2 is the total weight of mixture 

subject to observation, the moisture indicated is, very simply, 



°v 



mi = 



9*. 

9 



(109) 



(ra) Accuracy of Steam Calorimetry. — Along several lines error 
and unreliability may creep into the determination of quality of steam 
by the methods just given. These will now be briefly described, but 
not discussed in detail. 

The sample drawn into the calorimeter is likely to be far from 
representative of the current in the steam pipe. Moisture in excess 
of a very small proportion by weight tends to settle out or segregate, 
and the resulting nonuniformity will be greater when the pipe is hori- 
zontal, as the flow is slower, and when the steam is not stirred up by 
obstacles and changes of direction. It is best to place the sampling 
pipe in a vertical part of the steam line, and just beyond a bend; but 
in many cases the only sure thing is to have a separator in the line, 
weigh its discharge of water from the whole current, and use a calorim- 
eter to test the steam flowing from it. 

Loss of heat by radiation from the instrument will cause the indi- 
cated moisture fraction to be greater than that really existing in the 
steam tested; it lowers t 2 and h 2 in the throttling calorimeter, increases 



138 IDEAL STEAM CYCLE. [Chap. IV. 

#2 in the separator. Radiation is to be prevented as far as possible by 
nonconducting covering, and against what is unavoidable the instru- 
ment must be calibrated, by passing through it steam known to be 
dry; the results of the calibration are introduced as corrections in cal- 
culating from ordinary readings. 

Errors in thermometer indications, the greatest due to partial im- 
mersion in shallow thermometer cups, must be determined and allowed 
for. The measurement of temperature should be essentially correct, 
although extreme precision is not called for. 

There is considerable possibility that the steam in the low-pressure 
chamber of the throttling calorimeter may not be homogeneous, es- 
pecially if drops of water come in as a part of the sample. Experiments 
upon the heat required for superheating steam have shown, inci- 
dentally, that a small proportion of moisture may exist in a current of 
much hotter superheated steam for an appreciable time; and this con- 
dition would persist much longer with comparatively large masses of 
liquid than with the extremely fine mist produced by condensation in 
adiabatic expansion. The effect of this action will be to raise t 2 and 
h 2 above their true values, and its possibility is a strong argument 
against using the throttler alone with more than two or three per cent 
of moisture. 

The more detailed consideration of these matters, as also the de- 
scription of other schemes, belongs to a treatise on laboratory and 
experimental methods. 

§ 1 8. Special Graphical Methods 

(a) The Ideal Steam Cycle, whether for engine or turbine, takes 
the form of the Rankine cycle, Figs. 55, 56, 61, and 66. The quantities 
involved in calculations upon this cycle are set forth, in various rela- 
tions, in Tables II, VI, VII, and VIII. They are, temperature t, pres- 
sure p, specific volume v, condition, denned by quality x or superheat 
s = (t — t a ), total heat h or H, and entropy nor N. A scheme in which 
it is possible to combine all these in one diagram is now to be described 
and illustrated, although the diagram in shape for regular use is not 
made a part of this book. In the Rankine cycle, adiabatic or constant- 
entropy expansion is the determining requirement, and especial em- 
phasis is laid upon total heat. Entropy n and heat h are therefore 
made the coordinates of the diagram shown in Fig. 72, the Mollier 
diagram. 

(6) The Molliek Diagram. — Fig. 72 is intended simply to illus- 
trate this scheme; in a service diagram, a great many more of each 



§ 18 (&)] 



SPECIAL GRAPHICAL METHODS. 



139 



kind of line would have to be drawn. With the entropy in constant- 
pressure heating from 32 deg. fahr. as base, and with the corresponding 
total heat h as ordinate, curves are drawn for particular, constant values 
of each of the other four quantities named above. The first line plotted 
is the saturation line AA, with N from col. 13, H from col. 8, of 



1400 




1.56 n 1-60 1.64 1.68 1.72 1.76 

Fig. 72. — Outline of the Mollier Diagram. 



f.80 



1.84 



Table II. Below this, or in the region of wet steam, the lines of 
constant pressure and of constant temperature are identical, and they 
are straight lines because total heat and entropy vary together in 
constant ratio during vaporization. On these lines like AB it is easy 
to locate points for particular values of x, and thus get the constant- 
quality lines BB. Here the p and t lines are spaced for simple-number 
values of t, rather than of p. 



140 IDEAL STEAM CYCLE. [Chap. IV. 

For superheated steam, we have in Table VII intersections of lines 
of equal superheat, of equal temperature, and of equal pressure (the 
last corresponding to 10-deg. values of the saturation temperature), and 
can read off the total heat at each intersection. As an example, where 
pressure p = 67.0 (t a = 300), superheat s = 100, temperature t = 400, 
we read h = 1231.2. The same intersection can readily be located in 
Table VIII, and the entropy read as n = 1.6991. These values of n 
and h are the coordinates of the point C, the intersection of the 67-lb. 
p line, the 100-deg. s line, and the 400-deg. t line in Fig. 72. With enough 
of these points, the three sets of curves can be drawn. 

The lines of constant volume are laid out last. With a sufficient 
number of constant-pressure and constant-temperature lines drawn in 
the region of superheat, it is simplest to locate points from Table VI 
by interpolation between the isothermals in Fig. 72. For wet steam, 
we get x for a certain volume at a certain pressure, then find h for this 
x and go to the proper height on the p line in Fig. 72. 

(c) The Service Diagram. — In a regular reference diagram, the 
isothermals are commonly omitted, and the pressure lines are drawn 
for integral values of p, which gives them widely variant spacing, with 
numerous changes of interval. The volume curves differ so little in 
trend from the pressure curves, that if enough of both sets are put in 
for reasonably close interpolation, the mass of lines becomes rather 
confusing to the eye. Sometimes the diagram is printed in two colors, 
but a really accurate " register" of the two impressions seems to be 
hard to secure. To get both clearness and accuracy, the diagram must 
be to a large scale; and when there is room for this, it is exceedingly 
useful and convenient. Running down a line of constant entropy, we 
have right before us the changing pressure, volume, condition, and 
total heat, in adiabatic expansion. 

(d) Other Schemes. — It is evident that any two of the six quan- 
tities named in Art. (a) might be used as coordinates, after the 
manner of Fig. 72, and curves .be drawn for particular values of 
others. Thus in Table VII the coordinates are pressure and total 
heat, and lines are drawn for constant values of temperature and of 
superheat; on a larger diagram, constant-entropy lines could be added 
to advantage. In general, volume is the most difficult quantity to 
plot in a satisfactory way, especially in direct relation to pressure 
and temperature; with total heat for one coordinate, as in Fig. 72, it 
shows less extreme variation than in perhaps any other scheme of 
representation. 

These special graphical methods are most useful when a great 
many determinations are to be made, as in some extended investigation. 



§ 18 (d) SPECIAL GRAPHICAL METHODS. 141 

For the learner, the less concentrated methods exemplified in the pre- 
ceding sections are of more importance; as illustrating and enforcing 
principle, they should be thoroughly understood before coming to 
short cuts and labor-saving devices; and a clear understanding of prin- 
ciple will remove all difficulties in the way of intelligent use of such 
special devices. 

The Mollier diagram has its important field of usefulness in connec- 
tion with the steam turbine. Examples of its application in analysis 
of performance and in design of fundamental proportions will be found 
in § 48 (I) and § 49 (c)'. 



CHAPTER V 
ACTION OF THE STEAM IN THE ENGINE 

§ 19. The Indicator Diagram 

(a) Comparison of Actual with Ideal Diagram. — Continuing 
the line of the discussion in § 15, we now pass from the ideal steam 
diagram developed in Fig. 57 to the actual indicator diagram. The 
ideal diagram is modified in two principal directions: first, by resist- 
ance to the movement of the steam into and out of the cylinder; second, 
by the presence of clearance and compression. The thermal action of 
the cylinder walls has already been described in a general way in 
§ 15 (e) and is more closely discussed and analyzed in §§ 22 to 25. 

In Fig. 73, the indicator diagram ABCDEF represents the per- 
formance of the steam in the cylinder, and is to be compared with the 
circumscribed ideal diagram; which latter, however, is neither GHLQT 
nor JHLQP, but is shown in its true relative form in Figs. 74 and 75. 
The type of diagram in Fig. 73, chosen for illustrative purposes because 
the secondary effects now to be considered are all of good magnitude, 
is characteristic of the high-speed, noncondensing engine, with large 
clearance and with the steam distribution controlled by a single slide 
valve, so that high compression necessarily accompanies early cut-off. 
This is not an exact reproduction of an indicator diagram, because 
certain irregularities in outline, due to the instrument, are smoothed 
out; further, the curves of expansion and compression are taken to be 
simple equilateral hyperbolas. 

(b) Reference Lines. — The indicator draws the outline 
ABCDEFA and the atmosphere line TQ. The lines drawn about the 
diagram by hand, to get Fig. 73, are as follows: 

The vacuum line ON is parallel to the atmosphere line PQ, at the 
distance 14.7 lb. per sq. in., to scale, below it. 

The steam-pressure line JK is located by measuring the reading of 
the pressure gage from PQ upward. If this gage is on the boiler, per- 
haps at a considerable distance from the engine, the pressure difference 
GA is likely to be considerably greater than in Fig. 73, often rising to 

10 or 15 pounds. 

142 



§ 19 (&)] 



THE INDICATOR DIAGRAM. 



143 



The end lines GM and KN touch the diagram, marking off the 
length MN which represents the stroke of the piston or, to a suitable 
scale, the volume displaced by the piston in one stroke, also called the 
nominal cylinder volume. 

The distance MO is measured off to represent the clearance volume 
to this same scale, and the clearance line or pressure axis OJ is drawn. 
The clearance volume is made up of the space between the cylinder 
head and the piston (the crank being on dead center) together with 
the steam port or ports at one end. It is expressed as a fraction or 
percentage of the nominal volume, which is also the ratio of OM to MN. 

Finally the expansion curve is produced upward to meet the line of 
boiler pressure at H and downward to the end line at L. Very com- 
monly the pv = C curve is drawn along the expansion curve, in coin- 
cidence at a point just after cut-off, in order to see how nearly the 
actual curve conforms to this simple " standard." 




m 

Fig. 73. — A Sample Indicator Diagram. 

(c) Admission. — This operation begins at F; but the filling of the 
clearance space is so closely allied with compression that it can better 
be considered in that connection, in Art. (i). Starting at A, with the 
clearance filled, we note that the initial pressure in the cylinder is less 
than the outside steam pressure, because of the various resistances to 
flow of steam. In magnitude, the drop GA here shown is such as might 
be got by having the pressure gage on the steam pipe, near the engine 
■ — a very proper arrangement when the performance of the engine 
alone is to be measured and represented. For the present, however, 
we shall not distinguish steam-pipe pressure from boiler pressure. 

As the piston advances and the valve begins to close, the pressure 
falls off. Complete closure, or mechanical cut-off, is marked by the 
point B where the convex admission curve merges into the concave ex- 
pansion curve — or where the curvature reverses in direction. But ex- 



144 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

pressed in terms of the amount of steam admitted, rather than by the 
position of the piston when the edge of the valve meets the edge of the 
port, the effective cut-off is at H: the volume JH measures, at boiler 
pressure, the total amount of steam present in the cylinder. 

The admission line AB is really the resultant of the constant- 
pressure expansion GH in vaporization and the portion of the falling- 
pressure expansion from H to B. Because of all the resistances which 
the steam has to overcome in getting into the cylinder, there is a loss 
of available work equal to area GHBA. The action is of the nature of 
throttling, and at B the heat equivalent of this work has been added to 
the heat content of the steam. 

(d) Cut-off. — There are two ways of locating this and other 
events in the steam distribution. From the point of view of mechanism, 
with emphasis upon the fact that the valve closes when the piston is at 
the distance RB from the beginning of the stroke, we say that the ratio 
of apparent cut-off by the valve is 

C VA =|| '"•.•■• (U0) 

But in order to have a ratio of volumes, the clearance must be in- 
cluded; the volume back of the piston at cut-off is SB, while that at 
full stroke is ON. Then the real ratio of cut-off by the valve is 

CVr = q^- • (Ill) 

All distances and volumes are expressed as fractions of the stroke 
or of the nominal cylinder volume, represented by MN, which is taken 
as unity. If we let i stand for the clearance fraction, or the ratio of 
OM to MN, the relation results, 

CvE = ^j±i (112) 

In the figure, C V a = 0.35 and i = 0.10; then C YR = 0.45 + 1.10=0.409. 

Besides the two ratios of cut-off by the valve, or of actual cut-off, 
there are two corresponding ratios for the effective or ideal cut-off at 
H — which is called " ideal" because, if there were no losses of pres- 
sure from the boiler, and if the valve could act instantaneously, this is 
where it would close in order to determine the admission of the same 
amount of steam into the cylinder as by the actual cut-off at B. 

The apparent effective cut-off Cea = GH/MN is very nearly what 
is called the " commercial cut-off" in the Code of Rules for Steam- 
Engine Tests of the American Society of Mechanical Engineers — see 
Transactions, Vol. 24, 1903, page 749: the definition is modified by 
requiring that H shall lie on the line of initial pressure, which touches 



§ 19 (d)] THE INDICATOR DIAGRAM. 145 

the admission line AB at its highest portion. In other words, this 
commercial cut-off is the ratio of AK to MN in Fig. 74. 
The effective real cut-off, 

Cer = q^, (113) 

is an important quantity, being the ratio of the initial volume of all the 
steam in the cylinder, if at boiler pressure, to its final volume when the 
stroke is completed. 

(e) Expansion. — Of the shape of the expansion curve little need 
be said here, except to remark that it is seldom a true hyperbola, either 
rising above or falling below that curve, although not by any large 
amount under average conditions. In addition to the general de- 
scription of the thermal action of the cylinder walls given in § 15 (e), 
and in anticipation of the fuller discussion in the latter part of the 
chapter, it is now appropriate to describe briefly the means employed 
to control and minimize this action. 

By compounding the engine, or by dividing the expansion from 
boiler pressure to exhaust pressure into two or more successive stages 
in separate cylinders, the range of pressure and of expansion in the 
individual cylinder is ^diminished, with a marked decrease in initial 
condensation. 

By the use of a steam jacket, the cylinder walls are kept hotter and 
drier, and thus the freedom of heat transfer between the entering 
steam and the metal is decreased. The jacket consists of an annular 
space around the barrel or body of the cylinder, and of suitable hollows 
in the heads — see Fig. 203. It is filled with steam from the boiler, 
and provision must be made for draining out the water of condensa- 
tion. In the large, low-pressure cylinders of multiple-expansion engines, 
the pressure of the jacket steam is commonly reduced, chiefly from 
considerations of strength. 

The use of superheated steam has for its main purpose the diminu- 
tion of cylinder losses, which is effected by decreasing the freedom of 
heat transfer, through keeping the steam drier. Only with a very large 
excess of temperature does the steam remain superheated at cut-off 
and during expansion, so that there is little chance to utilize the greater 
available temperature range of the heat added in superheating, which 
is shown in Fig. 56. 

Increase of size, of speed, and of the quantity of steam admitted 
(later cut-off) all tend to diminish the amount or proportion of steam 
initially condensed. As regards the effect of these various devices and 
conditions upon the shape of the expansion curve, the general principle 
prevails that whatever diminishes the heat returnable during expansion 



146 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

tends to make the curve drop more rapidly after cut-off, and vice 
versa. 

It may be well to call attention to the point of usage, that in the 
language of the steam engine the term "expansion" is limited in appli- 
cation to the expansion with fall of pressure, from H or B to C in Fig. 
73. Of course, the constant-pressure expansion in vaporization, active 
at the surface of the water in the boiler and transmitted forward until 
it becomes effective upon the piston, is equally entitled to the name; 
but it is usual to let " admission "' cover this action. 

(/) Release and Exhaust. — The port is opened for exhaust 
before the stroke is completed, and the pressure falls along the release 
line CD as the steam is discharged. In the case of our sample diagram, 
about half the steam escapes from C to D, the rest during the constant- 
pressure exhaust from D to E. On account of the early release at C, 
there is a loss of work represented by the area CLD. This loss can 
hardly be avoided, for if the valve was kept closed till the end of the 
stroke, it could not be opened quickly enough to obviate a throttling of 
the release such as is shown by the dotted curve from L. 

The same causes that produce a loss of pressure during admission 
are responsible for the excess back pressure, which lifts the exhaust- 
line DE above PQ, and deducts another small portion from the area of 
the ideal diagram. . 

(g) Clearance and Compression. — After exhaust ends, at E, the 
low-pressure steam retained in the cylinder is compressed up to F by 
the piston; then fresh steam is let in, and the pressure in the clearance 
space is raised up to A before the piston makes any appreciable for- 
ward movement. The operation of admission consists, therefore, of 
two parts, the first the filling of the clearance space while the piston is 
practically standing still; the second the filling of the cylinder back of 
the piston as the latter advances, out to cut-off. Taking JHLQP as 
the ideal diagram (exactly like Fig. 57), the area JGFEP appears to be 
subtracted from it as the result of compression: but since the com- 
pressed steam so nearly fills the clearance space,* the volume of new 
steam is much less than JH (but little more than GH), so that the 
efficiency, measured by the ratio of work done to steam used, is not so 
very different from what it would be for the full diagram, back to the 
axis OJ. 

(h) Working Steam and Clearance Steam. — A clear under- 
standing of the effects of clearance and compression can be gained by 

* For the sake of simplicity, the effect of cylinder-wall action upon the volume 
of the clearance steam, during expansion, is not taken into account here: note remark 
in Art. (k). 



§ 19 (h)] 



THE INDICATOR DIAGRAM. 



147 



thinking of the steam in the cylinder as made up of two parts — the 
live or working steam which enters the cylinder to do work and escapes 
after the work is done, and the dead or clearance steam which, as a 
certain quantity, remains in the cylinder indefinitely, alternately ex- 
panding and contracting as the pressure changes. We can even imagine 
the latter body of steam to be separated from the working steam by a 
sort of light diaphragm, which will move back and forth in the cylinder 
like a loose auxiliary piston. When compression begins, at E in Fig. 
74, this diaphragm is against the piston, and so remains up to F; then 
the pistpn stops, and the compression of the dead steam is continued 
along the curve FU by the fresh entering steam. 

, G H. 




Kinetic Losses of Work Effect. 



(i) Filling the Clearance Space. — The raising of the pressure 
from F to A, Fig. 73 or Fig. 74, takes place while the valve is open but 
a very little way. The live steam, flowing through this narrow open- 
ing into a space where the pressure is lower, undergoes a regular 
throttling action, with some consequent loss of available energy. When 
the supplementary compression up to initial pressure is completed, the 
volume OV, Fig. 74, is filled with old steam and the volume VM with 
new steam. The latter, if admitted to drive the piston forward, could 
have done the work represented by the rectangle UAMV. Actually, it 
has done upon the clearance steam the pressure work FUVM (which 
can come back upon the piston during expansion), and has wasted the 
area AFU in noneffective acceleration of itself. 

(j) Kinetic Losses. — It appears now that the area AFU is to be 
added to the losses due to the moving of the steam, described in Arts, 
(c) and (/). The areas representing all these kinetic losses are shaded 
in Fig. 74. The steam-pipe effect GHKU shows pressure that was 
used up, in small part to produce the initial velocity of flow along the 
'ripe, in larger part to maintain this flow against surface friction and 
ihe retarding influence of bends and other obstructions. Area AKB is 



148 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



the loss caused by the throttling effect of the slide valve. The triangular 
figure CLD is only a small portion added to the loss of available energy 
due to incomplete expansion — all of this unused work (see area CHD, 
Fig. 57) going to produce a high velocity of the exhaust steam. Be- 
cause of the resistance of port and exhaust pipe, area DERQ is added 
to the losses incurred in moving the steam. 

(k) Action in Expansion. — As the pressure falls, toward and 
after cut-off, the clearance steam expands with the working steam. 
We now assume, as a rough first approximation, that the curve UFE 
is retraced in expansion, down to the lowest pressure. Actually, be- 
cause of condensation by the cylinder walls and shrinkage in volume, 
of which the clearance steam suffers its full share, the latter expands 
along a curve inside of UFE: further discussion of this matter will be 
found in §23, where the behavior of the clearance steam is more 
fully considered. With this steam retracing UFE, the effective vol- 






J G 




MO N 

Fig. 75. — The Diagram of True Expansion. 

ume of the active steam must be measured, at any pressure, from 
this curve — or from the position of an imaginary partition between 
the two bodies of steam. Since the reversed compression curve extends 
so far to the right, especially after it gets below the level of the release 
point C, it diminishes very considerably the amount of useful expansion 
realized in the cylinder. 

This action is most clearly shown by Fig. 75, which is derived from 
Fig. 74 through the rectification of the reference curve GFE, with 
horizontal shifting of the volume abscissas. Bringing the hyperbola 
GFE (Fig. 74) to the straight line GFE (Fig. 75), throws the zero line 
JO (Fig. 74) out to the hyperbola JP (Fig. 75). The scheme is most 
concisely defined, perhaps, by saying that in Fig. 75 volumes are shown 
as if measured, in both directions, from the imaginary dividing plane 
between the two bodies of steam, not from a fixed cylinder end. The 



§ 19 (k)] THE INDICATOR DIAGRAM. 149 

performance of the clearance steam is now shown by the curve JP, and 
ceases to be of much interest. 

(I) Effective Expansion. — The realized performance of the work- 
ing steam, freed from complication, is now given by the distorted dia- 
gram ABCDEF, shaded in Fig. 75 and in shape for direct comparison 
with the ideal diagram of Fig. 57. The true ratio of expansion is got 
by comparing the maximum volume RT with the initial volume GH. 
In Fig. 73, the apparent effective cut-off ratio, GH to MN, is 0.25; the 
ratio of volumes, including clearance, JH to ON, is 0.318; but the 
true effective ratio, GH to RT in Fig. 75, is 0.354, or the realized ratio 
of expansion is only 2.82. 

This last ratio is the most important piece of definite information 
supplied by the transformed diagram in Fig. 75. After we have gained 
from the latter the clearer idea of the performance of the working steam 
which it gives, we can go back to the original indicator diagram, and 
readily get from it this same ratio of effective expansion. By holding 
a scale parallel to the atmosphere line in Fig. 74 and moving it up and 
down — as with the diagram fastened down on the drawing board and 
the scale against the T square — it is easy to find by trial the greatest 
horizontal distance between the compression curve EF and the release 
line CD; and this maximum distance is the same thing as RT in Fig. 75. 
The initial volume GH is directly measurable on Fig. 74. 

(m) Form of the Compression Curve. — With a moderate amount 
of compression, say not more than enough to raise F halfway from T 
to G on Fig. 73, this curve agrees fairly with the hyperbola. But 
when compression begins early in the return stroke, so that the rela- 
tively small weight of clearance steam is raised well above the tempera- 
ture of the cylinder walls quite an appreciable time before fresh steam 
enters, there will be a marked abstraction of heat from this steam, with 
shrinkage in the value of the pv product and lowering of the upper 
part of the curve and of the point F. In extreme cases, the steam at 
F may be wetter than the whole body of steam at cut-off. This matter 
is more fully set forth in § 23. 

(ri) Information from the Diagram. — From the indicator dia- 
gram itself — that is, without the further knowledge obtained from a 
measurement of steam used — the following information can be de- 
rived : 

The form of the diagram shows the working of the valve gear, a 
matter which is not considered here, but is taken up in Chapter VIII. 
Also, from the shape of the curves of expansion and compression it is 
possible to draw some roughly approximate inferences as to thermal 
interactions, and perhaps as to leakage of steam. 



150 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

Having found from the diagram the mean effective pressure exerted 
upon the piston, it is easy to calculate the work done by the steam, or 
the indicated horse-power of the engine. The actually delivered or 
effective power — often called the brake horse-power, because it can 
perhaps be most exactly measured by means of the friction brake — is 
less than the indicated power by the rate of work absorption within the 
machine, against its own friction. The ratio of effective to indicated 
power is called the mechanical efficiency of the engine. 

From the fact that the properties of saturated steam, including 
specific volume, are fixed when the pressure is known, the engine can 
be made to serve as a volume-meter, to determine the quantity (weight) 
of steam used. Unfortunately, this measures only what is present in 
the cylinder as vapor, not what is also present as water, because of 
initial condensation. Between indicated and actual steam consump- 
tion there is always a considerable discrepancy. A true and reliable 
determination can be made only by a test in which the actual, total 
steam used is measured, either as water going to the boiler or, prefer- 
ably, as water formed by condensing the exhaust in a surface condenser. 

The subject of indicated power and steam consumption* will be 
taken up in § 21, while the closer study of the thermal action of the 
cylinder walls is carried forward in § 22. As a preparation for these 
discussions, a simple presentation of fact and principle in regard to the 
compound engine will now be made. 

§ 20. The Compound Engine 

(a) Objects of Compounding. — These can best be made clear 
with the help of an example. In Fig. 76, let the outline ABDEFG be 
the ideal steam diagram (like Fig. 57) for an engine to work between 
the pressure limits pi = 120 lb., p = 1.6 lb. In its length and narrow- 
ness, with a high ratio of maximum to average pressure, this diagram 
is open to the objections urged against the Carnot cycle with air in 
§ 8 (i), although it has the redeeming feature of a low back pressure. 
From the mechanical viewpoint, if the whole operation is carried out 
in a cylinder big enough to contain the final steam volume GF, the 
engine will have to be tremendously strong and heavy in order to carry 
the high pressure at the beginning of the stroke. From the thermal 
side, with the range of temperature from t\ to to, and with the very 
short cut-off, ratio e = AB/GF, the initial condensation by the cylinder 
walls will be excessive. 

These difficulties are very effectively overcome by dividing the 
expansion into steps or stages. The line JD is drawn at such a height, 






§ 20 (a)] 



THE COMPOUND ENGINE. 



151 



in Fig. 76, that it divides the area ABDEFG into about equal parts — 
in the final adjustment, areas ABCHJ and JDEFG are made equal. 
The work above this line is performed in the small, high-pressure 
cylinder; that below, in the large, low-pressure cylinder. Between the 
cylinders is placed an intermediate vessel or reservoir called the re- 
ceiver, now assumed to be so large that the pressure within it shows no 
cyclical fluctuation, due to the inflow and outflow of steam, but remains 
constant at the value represented by the height of line JD. The same 
considerations that demand and justify incomplete expansion for the 
whole engine — see § 15 (g) — are influential, although in lower degree, 
for the high-pressure cylinder. Instead of giving it the volume JD, we 
draw a line at PH to fix its volume; the exact location of this line is a 



120 

ioo- 

80- 
60- 
40 

p 

20H 



A IB I20=P, 
341 =t, 



J 19 Pz 225 t z Z 




M 
J 


b 


N 


6 


E 

If 


M 




N 



^^/P 




V 

Fig. 76. 



15" 



20 



W 



^5" 



K 



50 



Ideal Diagram for the Compound Engine. 



matter of judgment, involving as it does the sacrifice of the work-area 
CDH, through the pressure drop CH, which is called "receiver drop." 

The objects attained by this scheme for the effective utilization of 
a high ratio of expansion are, then, to get more uniform and less widely 
variant forces in the machine, and to keep the harmful action of the 
cylinder walls within reasonable bounds. 

(6) Cylinder Ratio and Separate Diagrams. — Almost uni- 
versally, different sizes or volumes of cylinder are obtained by the use 
of different diameters with the same stroke-length; in a very few special 
or freakish designs, the -strokes have also been different. In Fig. 76, 
JH is made one-fourth of GF, or the cylinder ratio GF to JH is fixed 
at 4 to 1 ; then the diameters are as 2 to 1. At a and b, the two parts of 
the main figure are changed to a form corresponding with ordinary 
indicator diagrams. An arbitrary base length MN is chosen, and the 



152 ACTION OF THE STEAM IN THE ENGINE. [Chap. 

low-pressure diagram JDEFG is shortened to this length, at b, but 
with no change of vertical measurement. In the stretching of the 
high-pressure diagram ABCHJ to the same length as the other, at a, 
there is an effect equivalent to the multiplication of its abscissas by 
the cylinder ratio, here 4. To compensate for this, and have the two 
diagrams a and b represent work to the same scale, the original ordi- 
nates of ABCHJ must be divided by the same ratio 4. 

Now there are two ways of looking at this high-pressure diagram 
with shortened ordinates. If the original scale is, say, 20 lb. to the 
inch, the new diagram will have a scale of 80 lb. to the inch when rep- 
resenting pressures on the high-pressure piston. Or, we may measure 
the shortened ordinates to the 20-lb. scale, and say that they then 
represent equivalent pressures on the low-pressure piston. In numeri- 
cal expression, with the particular proportions, a specific pressure of 
4 lb. (per sq. in.) on the small piston will produce the same total force 
and do the same work as 1 lb. per sq. in. on the large piston. According 
to the latter concept, with transfer of pressure and work from one piston 
to another, diagram a is said to be reduced to the low-pressure piston. 

Actual indicator diagrams follow, of course, the first idea above, in 
that each represents directly the variable pressure upon its own piston. 
It is neither convenient nor, in many cases, possible to choose springs 
whose scales are in the exact ratio of the cylinder volumes : but the idea 
of " reduction" of pressure from one piston to another has some im- 
portant applications, as will appear later. 

(c) Arrangement and Working of Engines. — In the stricter 
technical usage, the adjective " compound " is limited to engines with 
two stages of expansion, as in Fig. 76; ." multiple-expansion " is the 
more general term. An engine with three stages is called a triple 
expansion, one with four stages a quadruple-expansion. The highest 
number of stages ever used, in a few exceptional marine engines, is 
five. The degree of compounding (going back to the more general use 
of this term), is chiefly determined by the boiler pressure. In marine 
practice, with engines always run condensing, the ranges are about as 
follows, the line of historical progress being from the lower to the higher 
value in each case: 

Simple engines 30 to 70 lb. by gage 

Compound 80 to 120 " 

Triple 140 to 180 

Quadruple 200 to 250 " 



it u 

(( a 



In stationary practice, there is a tendency toward higher pressures 
for the same classes of engines, condensing compounds being run with 



20 (c)] 



THE COMPOUND ENGINE. 



153 



boiler-gage pressures of 120 to 150 lb.; while the compound locomotive, 
necessarily noncondensing, uses steam at from 200 to 225 lb. 

In the matter of getting the steam from one cylinder to the other, 
there are two typical cases. First, if the two pistons begin and end 
their strokes together, so that steam can pass from the higher directly 
into the lower cylinder, it is possible to get along without a receiver: 
this is called the direct-expansion compound. Second, if the two 
strokes are not timed together, as when there are two cranks at right 
angles to each other, the receiver is essential, and we call this a receiver- 
compound engine. 

Engines of the first class may have the cylinders placed in line 
(tandem) or side by side (parallel); and the connecting passages and 
low-pressure steam chest may amount to a considerable receiver space. 
An engine having cylinders side by side and cranks at an angle with 
each other is called a cross-compound. 




A 


"^ 


\! 






III. \ 








C 




A \ \ i 




D 


F 


( \ \ \ i 
\ \ \ \ 






M 


\ \ \ \\ 


G 


N 


\ V 




H 


y 


• 
• 

L 


y 
y 



M 



N 



Fig. 77. — Typical Cases of Receiver Action ; Ideal Diagrams, for cylinders having 

no clearance space. 

(d) Lines of Intermediate Pressure. — The characteristic effects 
of the changes in arrangement just described are illustrated in Fig. 77: 
all the variations occur in the lines which correspond to CH-HJ and 
JD in Fig. 76, that is, in the lines of intermediate pressure, between the 
cylinders and involving the receiver. The low diagram is placed be- 
neath the high, so that coincident timing appears directly in the first 
two cases and can readily be shown in the third. 

Case I. Direct-expansion engine, with no receiver. At C and G 
begins a common expansion in the two cylinders, which must continue 
clear to the end of the stroke, to F and J, in the ideal case of no clear- 
ance. In an actual engine there is low-pressure cut-off near the end of 
the stroke, and a short compression into the high-pressure clearance. 



154 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



Case II. Direct-expansion engine with a receiver. The receiver 
drop CD is followed by a common expansion DE and GH, to low- 
pressure cut-off at E and H. Then there is compression in the 
high-pressure cylinder and the receiver along EF and expansion in 
the low-pressure cylinder along HJ. 

Case III. Receiver-compound engine with cranks at right angles. 
Receiver drop CD is followed by compression in the high-pressure 
cylinder and the receiver, along DE, until the low-pressure cylinder is 
ready for admission at E and G: then comes a common expansion EF 
and GH, to low-pressure cut-off, which, as the simplest case, is taken 
to occur just at half-stroke. 

In cases II and III, the pressure at D is the result of a mixing of two 
bodies of steam, that in the small cylinder at pressure C and that in 
the receiver at pressure F. The most striking thing shown in Fig. 77 
is the characteristic difference between the forms of the high-pressure 
exhaust line DEF in cases II and III, which clearly distinguishes the 
two types of engine. 

For the detailed development of these diagrams, in the way of quan- 
titative relation and the exact form of the curves, the reader is referred 
to Steam Engine, Vol. II, Chapter XI, pages 449 to 476. In actual en- 
gines the ideal curves of intermediate pressure are very considerably 
modified by resistances to flow and similar influences, always in the 
direction of a more uniform pressure in the receiver. 




\ — tiL 


LC. >. ^1 


V 'V 


y J 




— 



Fig. 78. — Indicator Diagrams from a Compound Engine. Steam pressure near 
engine, 96 lb. by gage or 111 lb. absolute; condenser pressure, 22.2 in. mercury 
of vacuum or 3.9 lb. absolute; both pressure lines drawn on diagrams. Speed, 
250 r.p.m. Indicator springs, 60 lb. scale in high-pressure, 20 lb. in low-pressure 
cylinder. 

(e) Indicator Diagrams. — A sample set of diagrams from a 
compound engine, which is of the same type as the simple engine rep- 



§ 20 (e)] 



THE COMPOUND ENGINE. 



155 



resented by Fig. 73, is given in Fig. 78. The arrangement of the 
cylinders is outlined in Fig. 79, which also carries the essential dimen- 
sions. The size of a multiple-expansion engine is defined by giving 
the diameters in sequence, then the' stroke; this is a 13 and 20 by 16 
inch tandem compound. The arrows on Fig. 79 show the sequence of 
the cylinder ends in steam distribution; there is, of course, only a single 
passage from the high-pressure exhaust port to the low-pressure steam 
chest, but the steam from either end of the small cylinder gees into the 
opposite end of the large cylinder. The condenser pressure is found by 
subtracting the 22.2 in. of gage reading from 29.9 inches, the standard 
atmosphere, and reducing 7.7 inches to pounds of absolute pressure; 
the vacuum is very poor in this case, for it ought to be at least 26 or 27 
inches with proper working of the condenser. In the notation used to 
designate the diagrams, the first letter is for the cylinder, high or low, 
the second for the end, head or crank. The steam-distribution events 
are marked on Fig. 78, and a considerable inequality in the low-pressure 
cut-offs is apparent. 

Str oke: = 16" 
h.h. | 




Fig. 79. — Cylinder Arrangement of Tandem Engine. Clearance ratios, high head, 
0.16, high crank, 0.12, low head, 0.08, low crank, 0.06. 



(/) Combined Diagrams. — A most useful means of showing the 
action of the steam in a compound engine is the combined diagram, in 
which the separate indicator diagrams are brought to the same scales of 
pressure and of volume, and referred to the same axes — the operation 
being the reverse of the derivation of separate diagrams in Fig. 76. 
Two methods of combining will now be illustrated, the first fully de- 
fined by the statement just made, the second embodying in addition 
the idea of Fig. 75. 

In part I of Fig. 80, the indicator diagrams are prepared by dividing 
the length of each into ten equal parts, and erecting ordinates at the 
division points. At II the volumes, first of the clearances, next of the 
cylinders (nominal), are laid out from OP to a convenient scale, and 
the volumes MiNi, M 2 N 2 , are divided by lines corresponding to those 
on the diagrams in I. In this case, the pressure scale is the same as that 
of the low-pressure diagram, so that ordinates from the latter can be 
transferred directly; while those from the high-pressure diagram must 



156 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



be multiplied by three, or measured off three times. Using, if necessary, 
extra ordinates at the ends where the pressures are changing rapidly, 
we get a series of points through which the new curves can be traced, 
giving the result shown by the full-line figures. 




aid 1 



Fig. 80. — Diagrams Combined on Clearance Lines. 



On the original diagrams, hyperbolas are drawn through chosen 
points, marked E and C, on the expansion and compression curves: on 
the combined diagram, three of these are reproduced, all except that 
through E 2 . Instead of the latter, the curve through Ei is continued, 
in effect, so as to get a correct pv measure of the continuity of the ex- 
pansion. A horizontal line AD is drawn between the diagrams, the 
two upper hyperbolas cutting it at A and B, while that through C2 
meets it at D; then the length DF is made equal to BA, and the ex- 
pansion hyperbola is continued from F. Obviously, this is nearly as 
effective as the method of Fig. 75; for while it does not get rid of the 
clearance steam, it does eliminate the difference between the two quan- 
tities of this steam in the successive cylinders. 

Diagrams on the rectified compression hyperbolas, similar, to Fig. 
75, are dotted in on Fig. 80, but without any of the construction used 
in getting them being given. This would consist of a lot of horizontal 
lines along which the volumes, measured from the reference curves 
CiB, DC 2 , would be laid off from OP. The effect of indicator inertia 



§ 20 (/)] 



THE COMPOUND ENGINE. 



157 



upon the low-pressure compression curves is strikingly shown by the 
peculiar heel on the derived diagram: the indicator piston at first lags 
behind the rising pressure, then swings ahead of it, and keeps oscillating 
about the true pressure until its energy is absorbed in friction work. 
The hyperbola through C 2 should follow the mean of these waves. 

(g) Direct Combination on the Compression Lines. — This is 
illustrated in Fig. 81, where a graphical construction is used for trans- 




Fig. 81. — Diagrams Combined on Compression Curves. 

forming the volume ordinates to their new scales. The first step is to 
draw a number of similarly spaced abscissa lines on the indicator dia- 
grams and on the plane of the combined figure, at II. In the propor- 
tion diagram at III, AB is the actual length of the high-pressure dia- 
gram and BC is the corresponding volume to the scale of II, the same 
thing as MiNi in Fig. 80. After the diagonal AC is drawn, any abscissa 
as AD in I is laid off from A to D in III, and the intercept DE is the 
converted length, ready to be transferred to the position DE in II. 



158 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

Similarly, FA is the length of the low-pressure diagram, AG is the cor- 
responding volume to the scale of II, and F is the origin: FH is measured 
from F and HK is ready to be laid off in II. It is more convenient to 
use these proportion diagrams than to work through the first method 
of combination, as in Fig. 80. 

In Fig. 81, part II, a hyperbola is drawn through Ei, and cuts under 
the low-pressure expansion curve; but in Fig. 80 the hyperbola from F 
is well above its expansion curve. It appears then that the steam is 
not divided between the two ends of the low-pressure cylinder in the 
same ratio as between the two ends of the high-pressure cylinder. The 
only way to get a fair criterion of the total expansion is to draw a mean 
combined diagram. 

(h) The Average Combined Diagram. — In Fig. 82, the diagrams 
referred to the rectified compression hyperbolas are reproduced from 
Figs. 80 and 81 (in dotted line), with the irregularities on the com- 
pression side left out, and mean curves are partly drawn (in full line). 
Besides this averaging of the two ends, there is a change of volume 
scale, such that the diagram now represents the performance of one 
pound of steam: the method of determining the limiting volumes for 
this unit diagram is given later, in § 21 (Q, since it involves the rate of 
steam consumption by the engine. 

On Fig. 82 several reference curves are drawn, and at the right is a 
supplementary diagram of steam quality or condition during the re- 
spective operations of expansion. The hyperbola ABC is the first 
curve laid out, being made coincident with the high-pressure expansion 
curve just after cut-off. The low-pressure expansion curve rises above 
the hyperbola, which indicates considerable leakage through the high- 
pressure cylinder: it is normal for an unjacketed compound to show a 
shrinkage in the product pv from the high to the low cylinder, perhaps 
as much as 10 or 15 per cent. The curve DE is the line of constant 
steam weight for one pound of steam, or it is the saturation volume s 
plotted right from Table II. This is really the most useful simple 
curve that can be drawn for a reference line. An adiabatic from D 
would also be of interest, as the expansion line of the ideal Rankine 
cycle ; but drawing it generally leads to an unpleasing confusion of lines 
along the low-pressure diagram. 

*The quality curves FF and GG are got by taking x as the ratio of 
HK to HL, and laying it off to the scale at the bottom of the figure. 
Of course, this is only an approximation, less correct as the curves con- 
form less closely to pv = C and as the expansion and compression 
curves differ in form. It is better to draw the x curve for the total 
steam in the cylinder, including the clearance steam, as is done in Fig. 



§ 20 (h)) 



THE COMPOUND ENGINE. 



159 



115, for instance. An example of such curves for the common form of 
combined diagram, like Fig. 80, but on a stroke instead of a pressure 
base, will be found in Fig. 136. 

Finally, the hyperbola is plotted on the x diagram in curve A'C 




5 V 10 15 20 25 0.6 0.8 x \Q 

Fig. 82. — Mean Diagram for One Pound of Steam, from Figs. 80 and 81. 

(compare Fig. 52), and the adiabatic as D'J; here the curves are much 
clearer and less confused than on the pressure-volume diagram at its 
low-pressure end. 



§21. Horse Power and Steam Consumption 

(a) Mean Effective Pressure. — During the forward stroke, 
from M to N in Fig. 83, the steam does upon the piston the amount of 
work represented by the area ABCDNM; reducing this figure to the 
equivalent rectangle GHNM gives the mean total or forward pressure 
Vmi = GM. Similarly, during the return stroke the work done by 
the piston upon the steam is DEFMN, and the corresponding mean- 
back pressure is p mh or MK. Then the effective work, area ABCDEF 
or area GHLK, would be done by the action of the mean effective 
pressure p m or GK upon the piston through one stroke. 

In practice, p m is not got by subtracting p m b from p mf , but is 
found by measuring the area of the enclosed diagram ABCDEF with a 



160 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

planimeter. Dividing the area by the length gives the mean height, 
and multiplying this by the pressure scale of the ordinate gives the 
m.e.p. If a planimeter is not available, it is necessary to divide the 
diagram into a number of narrow vertical strips (of equal width), and 
take the average of the middle ordinates of the strips, measuring them 
as intercepts between the curves ABCD and FED. 

(6) Work per Revolution. — Although p m actually represents the 
difference between the two quantities of work done upon the piston in 
the two strokes which make up one revolution (one work is positive, 
the other negative), it is treated as if it were simply an unbalanced 
pressure acting upon the piston through the forward stroke. Then if 
A is the area of the piston in square inches and S the length of the 
stroke in inches, the work done in one end of the cylinder per revolution 
is, 

U = p m A~ ft. lb (114) 

In the other end of the cylinder there is done a similar amount of 
effective work, but generally not quite the same: how nearly alike the 
two m.e.p.'s will be depends upon valve action, and they may be very 
different if the valve gear is in bad adjustment; further, the area of the 
piston is reduced on one side by the cross section of the piston rod, so 
that generally the two A's are not the same. In any case, the sum of 
the two separate U's gives the total work per revolution. 

Note that the use of the ordinary m.e.p. does not give the work 
per stroke: to get this, we should have to subtract from the forward- 
pressure work on one face of the piston the simultaneous back- 
pressure work on the other face. But while the separate works per 
stroke would not, in general, be the same as the works in the two 
cylinder ends, the sum of either two would give the same total work. 

(c) Indicated Horse-Power. — Letting N be the number of rev- 
olutions or of double strokes per minute, the indicated horse-power 
developed in one end of the cylinder is 

12X33000 .' " ' vlltJ; 

Several partial i.h.p.'s having been found, as for the head end and crank 
end of the cylinder, the total power is got by taking their sum. 
The constant part of the horse-power formula, 

AS 
C = 12X33000' (116) 






§ 21 (c)] HORSE POWER AND STEAM CONSUMPTION. 



161 



is called the engine constant or cylinder constant. It can be worked 
out once for all in any particular case, and made a matter of record for 
the engine. 




Fig. 83. — Gross and Effective Work. 

(d) Cylinder Constants. — In Table 9, the first column is diam- 
eter D in inches, the second is the area A of this circle in square inches. 
In column 3, Vo is the volume in cubic feet of a cylinder D inches in 
diameter and ten inches long; and Co, column 4, is the engine constant, 
Eq. (116), for each ten inches of stroke length. To get the volume or 
displacement V in cubic feet, for any cylinder of diameter D and stroke 
length S, take V from column 3 and multiply it by S/10: to find the 
engine constant, follow the same procedure with Co. 

The small diameters in the first part of Table 9 are for the piston 
rod; their values are to be subtracted from those for the full piston 
diameter, before multiplying by S/10. 

Example 24. — Find piston areas, displacements, and cylinder constants 
for an engine 14 in. diameter by 15 in. stroke, with 2\ in. piston rod — or of 
a 14 X 15 — 2\ in. engine. 

The areas, from column 2 of Table 9, are 

Head end, A^ = 153.94 sq. in.; 

Crank end, A c = 153.94-4.00= 149.94 sq. in. 

The volumes, taking V from column 3 and with S/10 = 1.5, are 

Head end, V h = 0.8908 X 1.5 = 1.336 cu. ft.; 
Crank end, V c = (0.8908 - 0.0230) X 1.5 

= 0.8678X1.5= 1.301 cu. ft. 

Following the same method with C , the engine constants are found to be, 

Head end, C h = 0.003887 X 1.5 = 0.005831 ; 
Crank end, C c = (0.003887-0.000100) X 1.5 
= 0.003787x1.5=0.005681. 



162 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



Table 9. Cylinder Constants. 



D 


A 


V 


Co 


D 


A 


V 


Co 


1 


.79 


.0045 


.000020 


14 


153.94 


.8908 


.003887 


li 


.99 


58 


25 


14| 


165.13 


.9556 


4170 


i| 


1.23 


71 


31 


15 


176.72 


1.0227 


4463 


H 


1.49 


86 


' 38 


15| 


188.69 


1.0920 


4762 


l* 


1.77 


.0102 


.000045 


16 


201.06 


1.1636 


.005077 


■•■8 


2.07 


120 


52 


17 


226.98 


1.3135 


5732 


1^ 
x 4 


2.41 


139 


61 


18 


254:47 


1.4726 


6426 


1^ 
A 8 


2.76, 


160 


70 


19 


283.53 


1.6408 


7160 










20 


314.16 


1.8181 


7933 


2 


3.14 


.0182 


.000079 










2i 


3.55 


205 


90 


21 


364.4 


2.004 


.00875 


2| 


4.00 


230 


.000100 


22 


380.1 


2.200 


960 


2f 


4.43 


256 


112 


23 


415.5 


2.404 


.01049 


2| 


4.91 


.0284 


.000124 


24 


452.4 


2.618 


1142 


2f 


5.41 


313 


137 


25 


490.9 


2.841 


1240 


2| 


5.94 


344 


150 


26 


530.9 


3.073 


.01341 


21 


6.49 


376 


164 


27 


572.6 


3.313 


1446 










28 


615.8 


3.563 


1555 


3 


7.07 


.0409 


.000179 


29 


660.5 


3.823 


1668 


3| 


7.67 


444 


194 


30 


706.9 


4.091 


1785 


3| 


8.30 


480 


210 










3f 


8.95 


518 


226 


31 


754.8 


4.368 


.01906 


3! 


9.21 


.0557 


.000243 


32 


804.2 


4.654 


2031 


3f 


10.32 


600 


261 


33 


855.3 


4.950 


2160 


3f 


11.05 


639 


279 


34 


907.9 


5.254 


2293 


31 


11.79 


683 


298 


35 


962.1 


5.568 


2430 










36 


1017.9 


5.891 


.02570 


4 


12.57 


.0727 


.000317 


37 


1075.2 


6.222 


2715 


4| 


14.19 


.0821 


358 


38 


1134.1 


6.563 


2864 


4! 


15.90 


.0920 


402 


39 


1194.6 


6.913 


3017 


4f 


17.72 


.1026 


448 


40 


1256.6 


7.272 


3173 


5 


19.64 


.1136 


.000496 










6i 


21.65 


.1253 


547 


41 


1320.3 


7.640 


.03334 


51 


23.76 


.1375 


600 


42 


1385.4 


8.018 


3499 


5! 


26.00 


.1503 


656 


43 


1452.2 


8.404 


' 3667 










44 


1520.5 


8.799 


3840 


6 


28.27 


.1636 


.000714 


45 


1590.4 


9.204 


4016 


6| 


33.18 


.1920 


838 


46 


1661.9 


9.618 


.04197 


7 


38.49 


.2227 


972 


47 


1734.9 


10.040 


4381 


7± 

• 2 


44.18 


.2557 


.001116 


48 


1809.6 


10.472 


4570 


8 


50.27 


.2909 


1269 


49 


1885.7 


10.913 


4762 


81 


56.75 


.3284 


1433 


50 


1963.5 


11.363 


4958 


9 


63.64 


.3683 


1606 










91 


70.88 


.4102 


1790 


51 


2042.8 


11.822 


.05159 










52 


2123.7 


12.290 


5363 


10 


78.54 


.4545 


.001983 


53 


2206.2 


12.767 


5571 


10| 


86.59 


.5011 


2187 


54 


2290.2 


13.254 


5783 


11 


95.03 


.5500 


2400 


55 


2375.8 


13.749 


6000 


114 


103.87 


.6011 


2623 


56 


2463.0 


14.254 


.06220 


12 


113.10 


.6545 


.002856 


57 


2551.8 


14.767 


.06444 


12! 


122.72 


.7102 


3099 


58 


2642.1 


15.290 


6672 


13 


132.73 


.7681 


3352 


59 


2734.0 


15.822 


6904 


13| 


143.14 


.8284 


3615 


60 


2827.4 


16.363 


7140 



§ 21 (d)] HORSE POWER AND STEAM CONSUMPTION. 



163 



Table 9. — Continued. 



— 

61 


A 


V 


C 


D 


A 


V 


Co 


2922.5 


16.912 


07380 


81 


5153.0 


29.821 


. 13663 


62 


3019.1 


17.472 


7624 


82 


5281.0 


30.561 


. 13336 


63 


3117.2 


18.040 


7872 


83 


5410.6 


31.311 


.13013 


64 


3217.0 


18.617 


8124 


84 


5541.8 


32.070 


. 13994 


65 


3318.3 


19.203 


8380 


85 


5674.5 


32.839 


. 14330 


66 


3421.2 


19.799 


08639 


86 


5808.8 


33.616 


. 14669 . 


67 


3525.7 


20.403 


8903 


87 


5944.7 


34.402 


. 15012 


68 


3631.7 


21.017 


9171 


88 


6082.1 


35.198 


. 15359 


69 


3739.3 


21.639 


9443 


89 


6221 . 1 


36.002 


.15710 


70 


3848.5 


22.271 


9718 


90 


6361.7 


36.816 


.16065 


71 


3959.2 


22.912 


09998 


91 


6503.9 


37.638 


. 16424 


72 


4071.5 


23.562 


10282 


92 


6647.6 


38.470 


.16787 


73 


4185.4 


24.221 


10569 


93 


6792.9 


39.311 


.17154 


74 


4300.8 


24.889 


10861 


94 


6939.8 


40.171 


. 17525 


75 


4417.9 


25.566 


11156 


95 


7088.2 


41.020 


. 17900 


76 


4536.5 


26.253 


11456 


96 


7238.2 


41.888 


. 18278 


77 


4656.6 


26.948 


11759 


97 


7389.8 


42.765 


. 18661 


78 


4778.4 


27.653 


12067 


98 


7543.0 


43.651 


. 19048 


79 


4901.7 


28.366 


12378 


99 


7697.7 


44.547 


. 19439 


80 


5026.5 


29.089 


12693 


100 


7854.0 


45.451 


. 19833 



Example 25. — The diagrams in Fig. 84 are from a 14 in. by 15 in. engine, 
with 2 1 in. piston rod and with 8 per cent of clearance in each end, running 
at 225 r.p.m. on a steam pressure of 105 lb. by gage. The indicator had a 
spring of 60 lb. scale, or the pressure scale of the diagrams is 60 lb. per sq. in. 
to the inch of height. Analyze the steam distribution and calculate the 
indicated horse-power. 



ES3- 





Fig. 84. — Diagrams from a High-speed Steam Engine. 



The three important " events" in the steam distribution, cut-off, release, 
and exhaust closure or " compression," are marked on the diagrams by draw- 
ing short cross-lines, located by eye as closely as possible. Expressed in 
"apparent" measure — see § 19 (d) — or by their ratio of distance along the 
stroke line, and estimated from the beginning of forward stroke, or from the 
right end of the head diagram and from the left end of the crank diagram in 
Fig. 84, these events are as tabulated in Form 1. 



164 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



Form 1. Events in Steam Distribution. 



Diagram. 


Cut-off. 


Release. 


Compression. 


Head end 


0.31 
0.29 


0.86 
0.85 


0.37 


Crank end 


0.36 







Equilateral hyperbolas, pv = C, are drawn along both the expansion and 
the compression curves, being passed through the E and C points selected for 
the determination of indicated steam consumption, and laid out by the method 
of § 6 (g). The curves of the diagram conform very closely to the hyperbolas, 
and no comment is called for. 

The calculation for horse-power is outlined in Form 2. Usually, it is 
sufficient and more convenient to place the data for m.e.p. upon the diagrams 
themselves; these data are combined as explained in Art. (a). Using the 
engine constants already found in Example 24, i.h.p. is found through the 
multiplication of the constant by r.p.m. and by m.e.p., according to Eq. (115). 
Thus for the head end, 

H = 0.005831 X 225 X 48.35 = 63.43. 



Form 2. Calculation of Indicated Horse-Power. 



Cylinder end. 


Diagram 
area. 


Diagram 
length. 


Mean 
height. 


M.e.p. 


I.h.p. 


Ends. 


Total. 


Head 


2.50 
2.40 


3.10 
3.13 


0.806 
0.796 


48.35 
47.70 


63.43 > 

60.97) 




Crank 


124.40 



Example 26. — Calculate the indicated horse-power of the 13 and 20 by 
16-inch engine outlined in Fig. 79, with the diagrams in Fig. 78. 

The operations are indicated and results given in Form 3. The m.e.p. 's were 
found with an averaging planimeter, so that the areas of the diagrams are not 
recorded. 

Form 3. Indicated Horse-Power. 



Cylinder end. 


Piston 
area. 


Constant C. 


M.e.p. 


I.h.p. 


Ends. 


Cylinders. 


Total. 


H. H 

H. C 


132.7 
130.3 


0.005360 
0.005266 


26.7 
30.15 


35.8 1 

39.7 f 


75.5 






157.0 


L. H 


311.8 
309.3 


0.01260 
0.01249 


14.22 
11.75 


44.8 t 
36.7 J 


81.5 


L. C 









§ 21 (e)J HORSE POWER AND STEAM CONSUMPTION. 



165 



(e) Indicated Steam Consumption. — The data needed for calcu- 
lating this quantity are outlined on Fig. 85, and the method of pro- 
cedure will now be described. When the piston is at the position defined 
by the point E on the expansion curve, the space FE is filled with steam 
of the pressure p e and specific volume (dry saturated) s e . The volume 
FE or V e is preferably expressed by its ratio to the nominal volume or 




M 

Fig. 85. — Data for Indicated Steam Consumption. 

piston displacement V, which on the diagram is represented by the 
stroke line M.N. The relations involved are 



FE 

6 MN' 



V e = e7cu. ft.; 



and the weight of steam (vapor alone) present in the cylinder at E is 

w e = — = - X V. 

Sq Sq 

This measures the total steam; in order to deduct the clearance 
steam, similar expressions must be written for a point C on the com- 
pression curve, namely, 



c = 



DC 

MN 



cF, 



w c = - X V. 



Now for the net or working steam apparently used per revolution 
the value in pounds is 

w =w e - w c =v(- - -) (117) 

Letting K stand for the expression in parentheses, this formula becomes 

w = KV; (118) 

and since K = w s- V, it is evident that the quantity K is the indi- 
cated steam consumption per cubic foot of piston displacement. 



166 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

The simplest case in the determination of K occurs when the points 
E and C can be taken on the same horizontal line; then 

K= e -^> and (e-c)=g|: . . . . (119) 

but it is better not to take C much above the beginning of compression. 

(/) I. S. C. per Hour and per Horse-power-hour. — Now the 

piston makes 60 N outstrokes in one hour, N being the number of 

revolutions per minute, or the r.p.m.; then the i.s.c. in pounds per hour 

is I K = 60KNV (120) 

This is for one end of the cylinder, or for one diagram: a similar 
value would be found for the other end, and the sum of the two would 
give the total steam shown by the indicator. 

If we let Vb. stand for the total piston displacement in cubic feet 
per hour in both directions, so that 

7H = 6o#(y 1 + y 2 ), . (121) 

and find a mean value of K from the two diagrams, then the simplest 
way to get the i.s.c. per hour, total, is to substitute in 

/h = K m Vn (122) 

In terms of stroke and piston. area, 

7 = 1728 and 7h = K 28^' 

from Eq. (120); dividing this by the formula for i.h.p. in Eq. (115), we 

get 

7h_ 13750 

7 -ff-^T K ' (123) 



'm 



where In stands for i.s.c. per h.p.h. 

The method of Eq. (123) is generally used when isolated diagrams 
are worked up, while that of Eqs. (120) and (122) is preferable for long 
tests with fairly uniform conditions, especially if there is a parallel deter- 
mination of actual steam consumption. Note that in Eq. (123) all the 
dimensions of the engine have been canceled out, so that the quantity 
i" is dependent wholly upon the form of the indicator diagram. Note 
further that when two values of I have been found from a pair of dia- 
grams, their mean, not their sum, is to be taken to get a result for the 
whole engine; because each value is the ratio of the steam passing 
through one end to the work done by that steam. 

The point E may be located anywhere along the expansion curve, 
but is usually taken either just after cut-off or just before release. On 



§ 21 (/)] HORSE POWER AND STEAM CONSUMPTION. 



167 



account of reevaporation during expansion, the latter position will 
usually give a larger i.s.c. than the former. 

Example 27. — Calculate the indicated steam consumption from the dia- 
grams in Fig. 84, Example 25. 

The dimensions necessary for getting K are all marked on the figure. For 
the head end, e = 1.33 -^ 3.10 = 0.429, and with p e =90 lb., s e = 4.960. The 
whole calculation is set forth in Form 4. 

Form 4. Calculation of Indicated Steam Consumption. 



Cylinder end. 


e 


c 


Se 
Sc 


e 

Se 


c 

So 


Head 


0.429 
0.396 


0.339 
0.297 


4.960 
16.29 


0.0865 
0.0798 


0.0208 


Crank 


0.0182 



Cylinder end. 


K 


13750 
m.e.p. 


I.s.c. 


Ends. 


Mean. 


Head 

Crank . . " 


0.0657 
0.0616 


284.5 

288.0 


18.70) 

17.75 j 


18.23 



Here Eq. (123) is used, after K has been found, and the result is in pounds 
per horse-power-hour. If total indicated steam per hour is desired, results in 
Forms 2 and 4 can be combined as follows: 

I K = 124.4 (i.h.p.) X 18.23 (i.s.c.) = 2268 lb. Or, by the method of Eq. 
(121), after finding the K's take volumes from Example 24 and note that with 
225 r.p.m. the revolutions per hour are 13,500; then 



And 7 H = 



Head. Crank. 

V = 1.336 1.301 cu. ft. 

F H = 18036 17564 per hour. 

18040 X 0.0657 = 1185\ = 6 lb 



Cylinder volume, 
Piston displacement, 

/Head 

\Crank 17560 X 0.0616 = 1080^ 



(g) I. S. C. from Compound-engine Diagrams. — The indicated 
steam coefficient K is calculated from any one diagram, or for any 
cylinder end, in the same manner as for a simple engine. It is then 
rather the more direct procedure, in idea at least, to get the total i.s.c. 
or 7h by the method of Eq. (122), and divide by total i.h.p. or H. The 
calculation of the steam per horse-power-hour I directly from the dia- 
gram by the method of Eq. (123), is complicated by the fact that, in 
the multiple-expansion engine, the steam which is metered in one cylinder 
does work in two or more. In order to derive Eq. (123) through the 



168 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



division of /h by H, it is necessary that both these quantities be ex- 
pressed in terms of the same cylinder dimensions; and we have occa- 
sion to use the idea of reduced mean pressure, already developed in 
§ 20 (6). Supposs for instance, that K has been found from a high- 
pressure diagram: in this cylinder end, the mean effective pressure pi 
acts upon area A\, and the same steam then proceeds to do in the large 
cylinder the work represented by p 2 as m.e.p. on the area A 2 . Now the 
latter amount of work would be done upon the first piston by a reduced 
m.e.p. of the value, 

A 2 



Pt = P2j- = rp 2 , 



(124) 



acting on the area A\. In this formula, r stands, in general, for the 
ratio of the area upon which the pressure is actual to that to which it 
is to be reduced. Finally, a total m.e.p. of the value p m = p x + Pt, 
introduced into Eq. (115), will give the total i.h.p. developed by the 
steam, in terms of the dimensions of the high-pressure cylinder; which 
dimensions will then cancel out in the division leading to Eq. (123). 

With a three- or four-stage compound, there would be two or three 
reduced m.e.p.'s to be added to the actual m.e.p. in the cylinder end 
for which the i.s.c. was being found. 

Example 28. — Calculate indicated steam consumption from the com- 
pound-engine diagrams in Fig. 78, using horse-power results from Example 26 
as needed. 

The measurements required for this problem are marked on the diagrams 
as reproduced in Figs. 80 and 81. From these are calculated the values of K 
for each cylinder end, in Form 5, the E points being taken near high-pressure 
cut-off and low-pressure release, or near the beginning and the end of the total 
expansion. Then the i.s.c. is worked out, by the first method above, in Form 
6; the characteristic operation is the division of /h by H, or, for the high-pres- 
sure cylinder, of 2016 lb. of indicated steam by 157.0 i.h.p. Note how much 
larger / is for the low than for the high cylinder; as remarked in § 20 (h), this 
is abnormal and is due to leakage through or past the high-pressure cylinder. 



Form 5. Calculation of K, for I.s.c. 



Cylinder end. 


e 


Se 


c 


«0 


H. H 


0.438 
0.433 

0.977 
0.714 


4.894 
4.894 

26.78 
26.78 


0.316 
0.258 

0.244 
0.160 


8.50 
8.50 

38.40 
38.40 


H. C 


L. H 


L. C 





K. 



0.0895-0.0372 = 0.0523 
0.0885-0.0304 = 0.0581 

0.0365-0.0064 = 0.0301 
0.0267-0.0042 = 0.0225 



§ 21 {g)\ HORSE POWER AND STEAM CONSUMPTION. 



169 



Form 6. Ls.c. per Hour and per H.p.h. 



Cylinder end 



H. H 
H. C 

L. H. 
L. C. 



Cylinder 
volume. 


60iVFor 


K 


' 


s 


Ends. 


Totals. 


1.229 
1.207 

2.887 
2.860 


18,435 
18,105 

43,305 
42,900 


0.0523 
0.0581 

0.0301 
0.0225 


964 \ 
1,052 \ 

1,304 ) 

965 J 


2,016 
2,269 



/. 



12.84 
14.45 



The calculation of I from K by Eq. (123), with the use of reduced or re- 
ferred m.e.p. involving the relation expressed in Eq. (124), is set forth in Form 
7. The actual m.e.p. 's are first entered under p n , then each is multiplied by 
the volume ratio just ahead of it, and the result entered under p T , in the line 
belonging to the cylinder end in which is carried out the other part of the 
cycle. Thus for high head (H.H.), 26.70 X 0.429 = 11.47, and this is entered 
opposite L.C.; and so on. The rest of the calculation is obvious. The differ- 
ence between the two values of mean / in the low-pressure cylinder — 14.37 as 
found here and 14.45 in Form 6 — is due to the fact that the mean of the ratios 
of partial quantities is not the same as the ratio of the sums: the method of 
Form 6 is inherently the more correct. 

Form 7. Indicated Steam per Horse-power Hour Directly. 



Cylinder 
end. 



H. H 
H. C 

L. H. 
L. C. 



Volume ratio r. 



H. H. 



L. 
H. 


C. 
C. 


L. 
L. 


H. 

H. 


H 
L. 


C. 
C. 



H. H 



=0.429 



= 0.418 



= 2.39 



= 2.33 



Total M.e.p. 

+ Vx ■= Pn 



26.70+ (27.36) =54.06 
30.15+(34.00)=64.15 

14. 22+ (12. 60) = 26.82 
11.75+(11.47)=23.22 



13750 



254.1 
214.1 

512.4 
591.8 



A'. 



0.0523 
0.0581 

0.0301 
0.0225 



I.s.c. 



Ends. Means. 



13.29 
12.44 

15.42 
13.31 



12.87 



14.37 



(h) Measurement of Steam Consumed. — As intimated in § 19 
(n), the only way to find the amount of steam actually used by an 
engine is to weigh or measure that steam as water. The feed-water 
method is available when the output of one or more boilers can be 
wholly devoted to the engine under test, or, when, at least, steam is 
deflected only to small auxiliaries like the feed and condenser pumps, 
the exhaust from which can be condensed ancl weighed. This scheme 



170 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



is liable to the error caused by an insufficiently accurate determination 
or equalization of the amount of water in the boiler at the beginning 
and end of the test. The surface-condenser method gives the surer 
results, but calls for a supply and arrangement of apparatus which 
often is not available, except in a laboratory or special testing plant. 
In the more complicated engines there are a number of minor steam 
quantities to be measured, such as the amounts of water drained from 
the several jackets and receivers. 

(i) Curves of Steam Consumption. — In Fig. 86 are shown the 
two curves commonly used for representing the relation between steam 
consumed and power developed. Here indicated horse-power is the 
base, but effective power will serve equally well. Curve AA shows 
total consumption per hour, curve BB the consumption per horse- 
power-hour. The diagrams are most useful and effective when the 
amount of steam admitted per cycle is the principal variable, the limit- 
ing pressures and the speed being kept nearly constant as the load 
changes: some of the irregularities in Fig. 86, or the failures of the 
points to conform to smooth curves, are due to the variations in speed. 



5000 



4000 




Fig. 86. — Curves of Steam Consumption, representing tests of a 17 by 30 inch air 
compressor by Professors Denton and Jacobus. Trans. A.S.M.E., Vol. 10, 
1889, page 722. Controlling conditions: steam pressure, 89 to 92 lb. by gage; 
exhaust (into surface condenser) at pressure of atmosphere; speed about 60 r.p.m., 
except that tests 1, 8, and 15 are at higher speeds — see Fig. 90. The test 
numbers are from the original report. 



The curves in this figure are typical in form, well representing the 
characteristic behavior of the steam engine. As shown by curve BB, 
the steam S per horse-power-hour has a minimum which marks the 
condition of best economy (here at about 100 horse-power), and rises 



§ 21 (i)] HORSE POWER AND STEAM CONSUMPTION. 171 

from this in either direction, slowly at first, then at an increasing rate. 
The degree of underloading is sufficient in this series of tests to let 
excessive cylinder- wall action make S run very high. With heavier 
overloading there would be a similar marked rise of curve BB at its 
right-hand end, showing the loss due to an increasing lack of expansion 
after cut-off. Indicator diagrams from this engine are given in Fig. 90. 
and the effect of changes in condition will be more fully discussed 
presently. 

If the steam per horse-power-hour were constant over the whole 
range of loading, the curve AA would become a straight line, running 
to the origin of coordinates at 0. Drawing then the line CC, we can 
quite readily see from curve AA alone the manner in which extreme 
conditions make the steam rate rise above its best (lowest) value. 

(j) The Diagram of Specific Steam Consumption. — In order to 
eliminate speed and size of engine as factors in steam quantity — which 
is desirable for certain purposes — the scheme of Fig. 87 has been de- 
veloped. This follows the idea of curve AA, Fig. 86, in representing 
an absolute rather than a relative quantity; but, incidentally, the 
steam per horse-power-hour is also shown. The ordinate of the dia- 
gram is the steam consumed per cubic foot of piston displacement, the 
same kind of quantity as K in Arts, (e) and (/). To get it, the steam 
per hour, #h, is divided by Vb. = 60 NV: working for the whole cylinder, 
rather than for one end, V is taken as the double volume, or the volume 
displaced by the two piston faces in the two strokes which make up one 
revolution. With speed and size thus divided out, the rational ana- 
logue to horse-power is the mean effective pressure, and this is taken 
as the base in Fig. 87. 

The letter K will now be used as a general symbol for weight of 
steam per cubic foot of piston displacement, with subscripts to desig- 
nate particular values — note particularly that the various K quan- 
tities are in direct proportion to steam per revolution, being the latter 
divided by the nominal cylinder volume. The relation expressed in 
Eq. (123) holds between any K and the corresponding steam per horse- 
power-hour. Writing the equation as 

s== 13750^ ^ ■ (125) 

it appears that for any fixed value of S there is a straight-line relation 
between K and p m . The inclined lines radiating from zero on Fig. 87, 
marked with numbers which are values of S, come from this formula. 
The points along the curve SS show steam consumed, the same quan- 
tity as is plotted in Fig. 86 : referred to the scale at the left, they give 



172 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



values of K, while on the scale formed by the inclined lines values of 
S can be read off. The lower points show the steam condensed by the 
cylinder, and will be considered in the next article. 




005 



Fig. 87. — Specific Steam Consumption : weight of steam per cubic foot of piston 
displacement, plotted on mean effective pressure as base. Same engine and 
tests as in Fig. 86. Tests 1, 8, 15, and 31, indicator diagrams in Fig. 90. 



Example 29. — Engine 17 by 29f in., rods 2^ in. head end, 2f in. crank 
end. In test No. 1, m.e.p. = 65.42, r.p.m. = 70.38, i.h.p. = 153.0, steam per 
hour # H = 4571 lb., steam per horse-power-hour S = 29.88 lb. Find K as 
plotted on Fig. 87, also fix the ^-constant line for 30 pounds. 

First get V with the help of Table 9, as follows: 



Head. 

For the full piston, 7 = 1.3135 
For the rod, V = 0.0299 

Net value of V , 1.2836 



Crank. 

1.3135 
0.0376 

1.2759 



Adding and multiplying by S/10 (this S being " stroke," not " steam") we 
get, for the double displacement, 

V = 2.5595 X 2.975 = 7.615 cu. ft.; 

then V K = 60 X 7.615 XiV = 456.9 N cu. ft., this number 60 V being an im- 
portant engine constant in the present connection. 
The value of K is now, very simply, 

K = 4571 -v- (70.38 X 456.9) 

= 4571 -J- 32157 = 0.1422 lb. per cu. ft. 






§ 21 (J)] HORSE POWER AND STEAM CONSUMPTION. 173 

To locate the steam line for S = 30, one point is enough: let it be on the 
ordinate line for p m = 60, then from Eq. (125) 

K ~ 13750 13750 " °- ldU9 lb ' 

(k) Various Steam Quantities. — Consider the various lengths 
along the ordinate AB in Fig. 87; the quantities represented are as 
follows : 

AB or K is the actual steam consumed by the engine, the only 
quantity plotted in Fig. 86. 

BD or K{ c is the indicated steam at cut-off, the same as plain K in 
Eqs. (118) to (123); then 

AD or K mc is the " missing quantity," or the amount of steam con- 
densed by the cylinder walls, as determined at cut-off. 

Similarly, BE = Ki T and AE = K^ show indicated steam and con- 
densed steam at release, and ED is the amount of reevaporation. Some- 
times the last is a negative quantity, E falling above D; when this 
condition exists it is indicated by placing an arrowhead, pointing up- 
ward, on the line DE, or by placing a small arrow beside the points, 
as in Fig. 97. 

Finally, AF or K^ is the missing quantity at cut-off, computed by 
an empirical formula which will be presented and discussed in the next 
section. Without the second subscript, K\ and K m will be used as gen- 
eral symbols for indicated steam and for condensed or missing steam. 

In further illustration of the possibilities of the specific diagram, 
Fig. 88 is given at this point. Here a portion of the steam coming to 
to the engine is diverted into the jackets and reheater — the latter 
consisting of a nest of pipes or tubes placed within the receiver, for 
the purpose of drying and perhaps slightly superheating the steam 
going to the low-pressure cylinder. Both the jackets and the reheater 
are supplied with steam of full boiler pressure. Now, on the diagram, 

AB = K t = total steam consumed; 

AC = K = steam consumed in cylinder; 

BC = Kj = jacket steam. 

Note that the base in this figure is the m.e.p. reduced to the low- 
pressure cylinder of the compound engine. A new feature here intro- 
duced is the horse-power scale at the top of the diagram, laid out for 
the average speed of running, which is combined, of course, with the 
m.e.p. as scaled at the bottom. The main purpose of the diagram is 
the representation and study of steam quantity, especially of the sec- 
ondary quantities like K m and K } which are involved in the action of 
the cylinder walls. From this point of view an approximate idea of 



174 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



the power of the engine is enough, and when the speed varies only as 
permitted by the governor, the horse-power scale gives the load quite 
effectively. In the engine whose performance is represented by Fig. 
88, the speed varied from 120.6 to 122.7 over the range of loading, or 
by 1.7 per cent. 



0.03 




M.E 



10 REF. TO 20 LP. Cyl. 30 



Fig. 88. — Tests of a 20 and 40 by 42 inch Corliss Cross-compound Engine, with 
steam jackets and a reheating receiver. D. S. Jacobus, Trans. A. S. M. E., 
Vol. 24, 1903, page 1274. No. 26 in Table 13, page 268. 

(I) The Unit Steam Diagram. — Having the specific steam con- 
sumption K, it is an easy matter to get the length of volume base for a 
steam diagram to represent the performance of one pound of steam. 
If the engine consumes K lb. of steam per cubic foot of piston dis- 
placement, the displacement volume corresponding to a consumption 
of one pound of steam is evidently 1 , •£■ K. Thus in Example 29, K 
is found to be 0.1422 lb. per cu. ft.; then the base length MN (repre- 
senting the stroke line, not including clearance length) is 1 -f- 0.1422 = 
7.03 cu. ft., which is used in Fig. 90. 

In the case of Fig. 82, a slightly different procedure is more con- 
venient. As the engine had not been tested for steam rate, it was 
necessary to assume (for illustrative purposes only) a probable value of 
steam consumption. This was taken as 17.5 lb. per h.p.h., which is 
probably too low, in view of the strong indications of leakage. With 
157.0 i.h.p. (from Example 26), the hourly rate is W h = 157 X' 17.5 = 
2748 lb. of steam; and at 250 r.p.m. the number of cycles is 30,000 per 
hour. Then the consumption of steam is 2748 -f- 30,000 = 0.0916 lb. 
per cycle. If now the diagrams with actual engine volumes represent 
the performance of 0.0916 lb. of steam, the unit diagram must be larger 
in the ratio of 1.00 to 0.0916; or, the volume measures from Figs. 80 and 



§ 21 (I)] HORSE POWER AND STEAM CONSUMPTION. 175 

81 must be multiplied by 10.92 before they are laid off to scale in Fig. 
82. To get the limiting volumes OM and MN in the usual diagram 
like Fig. 80 (full-line), the actual volumes of displacement and clear- 
ance would be multiplied by this factor. 

§ 22. Effect of the Cylinder Walls 

(a) General Conditions of Knowledge. — A great deal of in- 
formation has been accumulated as to the resultant effect of the cylinder 
walls upon the performance of the steam in the engine, but in regard to 
the intimate detail of the thermal interchanges we have very little 
exact and reliable knowledge. With good indicator diagrams and a 
careful measurement of steam consumed, it is a comparatively easy 
matter to determine the net effect of the wall action, as represented by 
the magnitude and manner of variation of the missing quantity, or of 
the difference between actual and indicated steam: the methods re- 
quired have just been developed. It is not at all difficult, although 
more troublesome, to go a step farther, and from these same data 
deduce the amounts of heat transferred back and forth, between steam 
and metal. The problem in thermal physics, for the rational, synthetic 
solution of which both method and data are almost completely lacking, 
would be stated about as follows: 

Given an engine with a known volume of cylinder and area of in- 
ternal surfaces, working through a certain range of pressure and of 
steam temperature, and with the time and timing of the cycle fixed by 
the general speed of running and by the action of the valve or valves; 
with these data, find how much the temperature of the metal will vary, 
how much heat will be interchanged between steam and metal, and 
what amount of initial condensation will occur. 

In the present section, the question of cylinder losses is quite fully 
studied, by the empirical method of comparing and combining results 
as to the missing steam; that which follows is devoted to the effect of 
compression upon economy. In § 24 the methods of thermal analysis 
are described and illustrated, while § 25 summarizes the comparatively 
small amount of data available in the direction of a solution of problems 
like that just stated. 

(6) A Formula for Cylinder Condensation. — The writer has 
devised a formula for the proportion of initial condensation, which 
harmonizes the variant data about as well as can be expected, and has 
a wide range of application. The formula is 

m = ^=\/— ; (126) 



176 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

in which 

m is the fraction of initial condensation, or the ratio of the missing 
quantity to the total steam; commonly, and most conveniently 
this base is the steam entering the cylinder; so that in terms of 
Fig. 87 and the definitions in § 21 (k), m is equal to K mc /K. 
But when there is a great deal of compression, or a large 
relative weight of compressed steam, m is to be considered as 
the ratio of the missing quantity to the total weight of sub- 
stance present during expansion. 
C is a constant or coefficient, which must be changed to some 
extent with the type of engine; a good mean value is 0.27, and 
the ordinary range is from 0.25 to 0.30. 
N is the speed of running, in revolutions per minute. 
s is a constant obtained (for any engine) by dividing the surface 
of the nominal cylinder in square feet by its volume in cubic 
feet; this factor is an approximate inverse measure of the size 
of the cylinder. 
T represents the range of steam temperature within the cylinder 
during the cycle, from the highest pressure p\ to the lowest 
pressure p 2 , these pressures being taken from the indicator 
diagram. It is more fully defined on page 178. 
. p is the absolute pressure at the point E, on the expansion curve 
at or just after cut-off, for which the indicated steam con- 
sumption is found. 
e representing the ratio of cut-off or the amount of expansion in 
the cylinder, has the same meaning as in the calculation of 
indicated steam consumption; it is the total volume out to E 
divided by the nominal cylinder volume V. 
The formula is intended to give the missing quantity at cut-off, in 
an engine which is tight enough to show but an inappreciable amount 
of leakage at valves and piston, tested when standing still, in the usual 
fashion — see Art. (p). The engine is supposed to receive ordinary, 
"commercially dry" steam, which generally shows from 0.5 to 1.5 
per cent of moisture when tested with the throttling calorimeter. The 
formula is not applicable to the lower cylinders of multiple-expansion 
engines, except in the few cases where the water in the exhaust from the 
high cylinder is allowed to separate out in the comparative quietude of 
a large receiver and is drained away, leaving dry steam to enter the 
lower cylinder. It does not cover the use of superheated steam, nor 
does it apply when steam jackets are in action. 

(c) Basis of the Condensation Formula. — Equation (126) is 
rational as to the elements involved, but empirical as to the amount of 






§ 22 (c)] EFFECT OF THE CYLINDER WALLS. 177 

influence which each exerts; it is justified, of course, only to the degree 
in which its results agree with those of reliable experiments. Three 
major considerations have been incorporated into the formula, namely, 

1. The time of the whole cycle, proportional to l/N. 

2. The amount of metal surface exposed per unit of steam affected, 
taken as roughly proportional to s/pe. 

3. The range of steam temperature within the cylinder, represented 
by T. 

(1) The strength of the time influence is purely empirical; in close 
analysis it appears that the exponent of the divisor N ranges from 0.3 
to 0.4, but J, or the cube root, is found to be quite a satisfactory 
mean value. 

(2) It would be logical to use the whole clearance surface — cylinder 
head plus piston face plus port surfaces — together with the portion of 
the cylinder barrel out to cut-off, and compare this with the total 
amount of steam admitted or present, including that condensed. As 
regards the cylinder, this would require information which usually is 
not available; while on the side of steam quantity most undesirable 
complication would be introduced into what can be, at best, but an 
approximate estimate of the missing quantity. The actual procedure 
is as follows: 

The specific volume of steam is taken to be nearly proportional to 
1/p, so that pe represents the indicated steam per cubic foot of dis- 
placement, or K 1C . As defined above, s is the nominal surface per 
cubic foot of displacement; then s/pe is at least roughly proportional to 
the surface per pound of steam. The useful assumption is not so much 
that s represents actual clearance surface as that it varies in about the 
same manner with size of cylinder. Letting D be diameter and S 
stroke of piston, both in inches, and using for the total surface two 
circles of diameter D plus the cylindrical barrel of length S, we have, 



144 \ 2 ' / 4 1728 

-@+-)*S?-S(»St*)- ■■-.<-> 

(3) It is apparent that the amount of heat interchange between 
steam and cylinder walls will depend upon the range of temperature in 
the cylinder. But it was found that the very large increase in range 
caused by dropping to condenser temperatures exerted too great an 
influence in the formula; while in the first cylinder of a multiple-expan- 
sion engine the range was too small to account for the condensation. 
To use the range of pressure would give an error in just the opposite 



178 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



direction, making the " moisture" figure out too small with condensing 
engines, too large with compounds. 

To get around this difficulty, at the same time avoiding any com- 
plex mathematical expression in terms of temperature, the artificial 
function T was laid out by trial; this is shown in Fig. 89, plotted on p 
as a base, with the temperature curve (from Table I) dotted in for 
comparison. To get T for the formula, look up 7\ and T 2 , correspond- 
ing to the highest and lowest pressures in the cylinder, then 

T = T 1 -T 2 (128) 

Do not confuse this T with the absolute temperature. 



\J\J\J 














— 
















i 
1 




r J -~ 








i 


i — 






j 
































































































































































































400 
























































— 




— 










































, 


— - 


- — 


— "" 








































T 








,- 


-— 


-" 




















































> 




t 


















































f^ 




■ 






































300 
















,--?- 
























































ft 


sis 
























































> 


/ 




















































°r 






/ 


/. 


























































- 


// 
























































200 




f 


























































/ 






























































7 






























































/ 
i 






























































/ 




























































100 


/ 





























































50 p 100 150 200 250 

Fig. 89. — The Temperature Function T. 



300 



Example 30. — Same engine as in Example 29, 17 by 30, mean clearance 
0.071, double slide valve (Meyer gear — see Fig. 252). In Test No. 10, 
Pi = 108.1, p 2 = 16, both absolute, N = 58.0, cut-off is at 0.313 of stroke and 
at 80.5 lb. abs. Compute the probable condensation ratio m. 

From a handbook table of powers and roots, or from the slide rule, 



By Eq. (127), 



</N = ^58.0 = 3.87. 



_ 12/34 



7V30+ 4 =^^ = 3.62, 



0.27 V's = 0.514. 

From Table 10, - 

Vi = 108.1, T x = 341.1 
p 2 = 16, T 2 = 212.0 



T = 129.1. 



§ 22 (c)] 



EFFECT OF THE CYLINDER WALLS. 



179 



From the cut-off and clearance as given. 

e = 0.313 + 0.071 = 0.384, pe = 30.9. 
By Eq. (126), 



m 



_ 0.514 /129.1 

3.87 V 30.9 " U ^ 7L 



According to the report of the tests — see reference under Fig. 86 — the 
fraction of steam not accounted for by the indicator is, at cut-off, m c = 0.264, 
at release, m r = 0.211, so that in this case the formula shows most excellent 
agreement with the test. Use of the slide rule is especially appropriate and 
convenient in the above calculation. 



Table 10. Values of T for Equation (126), 



V 


T 


V 


T 


V 


T 


V 


T 





170 


45 


262 


115 


348 


185 


409 


1 


175 


50 


269.5 


120 


353 


190 


413 


2 


179 


55 


277 


125 


358 


195 


416.5 


3 


183 


60 


284 


130 


362.5 


200 


420 


4 


186 


65 


291 


135 


367 


210 


427 


6 


191 


70 


297.5 


140 


371.5 


220 


434 


8 


196 


75 


304 


145 


376 


230 


441 


10 


200 


80 


310 


150 


380.5 


240 


447.5 


15 


210 


85 


316 


155 


385 


250 


454 


20 


220 


90 


321.5 


160 


389 


260 


460.5 


25 


229 


95 


327 


165 


393 


270 


467 


30 


238 


100 


332.5 


170 


397 


280 


473 


35 


246 


105 


338 


175 


401 


290 


479 


40 


254 


110 


343 


180 


405 


300 


485 



p is absolute pressure in pounds per square inch. 
T is the temperative function in degrees fahrenheit. 

(d) Various Engine Tests. — As already remarked, an empirical 
formula like Eq. (126) is justified only in so far as it fits the facts, or 
agrees with experimental data. A number of important sets of engine 
tests will now be diagrammed and briefly described, with the double 
purpose of showing actual performance and of trying out the conden- 
sation formula. The method of Fig. 87 is used, the missing steam 
being represented, not by the ratio m, but in actual magnitude as K m 
or mK. Conclusions or summarized statements will be found in Arts. 
(o)> (i)j (I)) ( n ), an d (0), while leakage is discussed in Art. (p). A 
further presentation of data, in condensed numerical form, is made in 
Table 13, § 27 (j). 

It must be fully understood that the probability of a definite and 
closely-acting law, relating the amount of cylinder condensation to the 
controlling conditions, is rather low. Nevertheless, the development of 
a fairly good approximation is of great advantage and utility. The 



180 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



applications of the formula are two: it may be used to predict or esti- 
mate the probable actual consumption from the data of a simple indi- 
cator test of an engine; and it will serve as a standard of comparison 
in steam-rate tests of working engines, upon which to base an estimate 
as to how much of the missing quantity is due to leakage. Further, 
in the discussion of test-series where there are changes in other than 
the principal variable, the use of K mi from Eq. (126) as a standard of 
comparison for observed K mc practically eliminates the effect of these 
secondary changes. 

In any particular engine, the controlling conditions are the two 
limiting pressures, the ratio of cut-off, and the speed. Variation of 
cut-off with load is the commonest change, in power service at least, 
and that type of variation will be considered first. 

(e) Variation with Cut-off. — Fig. 87 is a very good example in 
this connection, to be accompanied by the indicator diagrams in Fig. 
90. On the latter figure,- the speeds are given under N and the i.h.p.'s 



100- 




FiG. 90. — Steam Diagrams from a 17 by 30 inch Noncondensing Engine, mean 
clearance 0.071, tests plotted in Figs. 86 and 87. Mean indicator diagrams at a, 
unit diagrams at 6: in regard to layout of the latter, see § 21 (I). 

under H ; while A U is the indicated work output per pound of steam, 
or the net external work of the steam, expressed in heat units. The 
thermal value of one horse-power-hour being 2545 B.t.u., and the 
engine consuming S lb. of steam per h.p.h., the output per pound is, 

AU = 254:5 + S (129) 

The curve SS is the saturation line, or the curve of constant steam 
weight for one pound of steam. The distance between this line and 



§ 22 (e)] 



EFFECT OF THE CYLINDER WALLS. 



181 



the expansion curve of any diagram does not exactly represent the miss- 
ing steam, because the steam back of that curve includes the clearance 
steam, in addition to the pound of working steam. To get a true 
measure of quality, it would be necessary to produce the compression 
curves upward — in idea, as curves of constant steam weight, but, with 
such proportions as here exist, about equally well as hyperbolas — then 
divide the intercept between expansion and compression curves by the 
distance from the vertical axis to SS. Compare the compound-engine 
diagrams in § 27. 

In Fig. 87, the fraction m ranges from 0.14 in test 2 to 0.55 in test 
32. Roughly, the quantity K mc is nearly a constant, falling off slightly 
toward both ends of the range of m.e.p. Fig. 90 makes clearly evident 
the way in which the increasing relative size of the missing quantity 
cuts down the effective work area, soon neutralizing the gain from 
longer expansion. Test 8 shows about the condition of best efficiency, 
as appears also from its location on Fig. 87. 

There is a strong element of historical interest in the tests set forth 
by Figs. 91 and 92, since these experiments were among the first clearly 




Fig. 91. — Tests of 36 by 96 in. Low-pressure Condensing Engine, U. S. S. Michigan, 
made in 1860. Isherwood, Researches in Steam Engineering, Vol. I, pages 91 
to 120. Paddle-wheel revenue cutter, duplex engine, one cylinder used in tests, 
vessel moored to dock. Boiler pressure 20 lb. by gage, speed 11 to 21 r.p.m. 
I. s. c. recomputed with present steam tables. For scheme of diagram, see 
Fig. 87. 



to establish the fact and the harmful effect of cylinder condensation, 
showing that there is an early limit to the amount of expansion that 
can economically be carried out in one cylinder. In Fig. 92, the shrink- 
age of volume is more striking than -in Fig. 90. Here hyperbolas are 
drawn along the expansion curves, on the two diagrams with earlier 



182 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



cut-offs, also the very short compression curves are produced upward. 
The saturation curve is for one pound of steam, as in Fig. 90. Fig. 91 
shows that K mc holds nearly constant for tests 1 to 5, then falls off quite 




Fig. 92. — Unit Diagrams from the Michigan's Engine, Tests 1, 4, and 7. Clear- 
ance, 0.058; range of cut-off, 0.09 of stroke at 33 lb. abs. to 0.92 at 32 lb. 

sharply. The formula points agree fairly well with a horizontal straight 
line, as against a slightly inclined line in Fig. 87. To make K m i equal 
K mG on an average of the seven tests, 'constant C in Eq. (126) would 
have to be raised to 0.30; while for average conformity in tests 1 to 5, 
the coefficient must be made a little over 0.34. 

(/) Other Series of Tests in which cut-off is a principal variable 
are diagrammed in Figs. 93 to 97. To supplement the showing of Fig. 



OJSr 1 




0.05 



Fig. 93. — Tests of an 8 by 24 in. Noncondensing Corliss Engine, Massachusetts 
Institute of Technology, about 1884; Peabody's Thermodynamics, earlier editions, 
also Trans. A. S. M. E., Vol. 7. Clearance, 0.04; range of cut-off in main group 
of tests, from 0.03 of stroke at 74 lb. abs. to 0.24 at 72 lb. For scheme of dia- 
gram, see Fig. 87. 

87, the performance of a very small Corliss engine is given in Fig. 93. 
The ratio m c runs very high, ranging from 0.43 to 0.70, yet the formula 
value mi keeps close to it. The minor groups, of three tests each, show 



§ 22 (/)] 



EFFECT OF THE CYLINDER WALLS. 



183 



the gain from superheating in this engine. The amount of superheat 
varied from 103 deg. fahr. at the heaviest load to 175 deg. at the light- 
est. With so much room for saving, superheating effects a marked 
reduction in the steam used. 

As examples of large, low-pressure engines at high speeds, the per- 
formance of the low-pressure cylinders of a group of compound engines 
is given in Fig. 94. By draining the receiver and weighing the water 
thus drained out, dry steam is supplied to the low cylinder in known 




18 20 



Fig. 94. — Large Low-pressure Condensing Engines; low-pressure cylinders of 
engines in the Marks tests, Fig. 97. Range of size, from 38 by 42 in. at 120 
r.p.m. to 60 by 56 in. at 100 r.p.m. Initial pressure (within cylinder), 16 to 
32 lb. abs., exhaust pressure 1.7 to 3.4 lb. abs. Range of cut-off, 0.14 "to 0.47 
of stroke. 



amount, so that the latter can be treated as a simple engine, with its 
own m.e.p. and steam consumption per h.p.h. Of the full set of tests 
shown in Fig. 97, only those are here plotted in which the jackets and 
reheater were out of action. Except for engine B, the most erratic in 
Fig. 97 also, there is excellent agreement between formula and ex- 
periment. In these engines, K m is less at light loads because the 
initial pressure (the receiver pressure in the whole engine) falls as the 
load is less and the high-pressure cut-off is earlier, so that the tempera- 
ture range in the big cylinder is less. 

The next example, Fig. 95, is complicated by the addition of tests 
made with the jacket, which are plotted as in Fig. 88. Unjacketed, 
K mi and K mc agree quite well. With the jackets (on heads and sides), 
it appears that at late cut-offs the saving in condensation within the 



184 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



cylinder is neutralized by the condensation in the jacket; but with 
earlier cut-off and a larger margin of possible saving, the jacket has a 
useful effect. 

60 70 



0.15 



1.0 I. H P AT 30 85 R .P.M. 50 



0.10 




0.05 



Pm 40 60 80 

Fig. 95. — Tests without and with Jackets, 9 by 36 in. Corliss Engine, speed about 
85 r.p.m.,' initial pressure 112 lb. abs., exhaust pressure 6 lb. abs. (these are 
pressures in the cylinder — the engine was run condensing, but with a poor 
vacuum). High-pressure section (alone) of the triple-expansion engine at 
Sibley College, Cornell University. R. C. Carpenter, Trans. A. S. M. E., 
Vol. 16, 1895, page 924. Range of cut-off, 0.01 of stroke at 66 lb. abs. to 
0.40 at 104 lb. Clearance 0.076. For scheme of diagram, see Figs. 87, 88. 

Fig. 96 represents tests made by Mr. Willans upon one of his cen- 
tral-valve engines, of small size. Those shown here are under the dis- 
advantage, for present purposes, that change in cut-off is accompanied 
by change in one of the limiting pressures, either pi or p 2 , sometimes 
in both. The first three groups in the first report, on noncondensing 
tests, are plotted in Fig. 96, where the ordinates are marked with the 
original designating numbers. According to this notation, the first num- 
ber is the intended initial absolute pressure in the cylinder, the second 
the intended ratio of expansion. It appears that K mi runs low in the 
simple engine, high in the compound and triple. Because of the high 
speed (400 r.p.m.), the missing quantity is relatively small, therefore 
the differences between K mi and K mc are of a low order of magnitude in 
comparison with the total steam measured. These are feed-water 
tests of a small engine, and the probability that the irregularities in the 
differences between the i£ m 's are due to small errors in the feed-water 
measurements makes it hardly worth while to attempt any deductions 
from these differences. 






§ 22 (/)] 



EFFECT OF THE CYLINDER WALLS. 



185 



Largely with the purpose of showing the kind of results got under 
service conditions, with large and well-maintained engines, the group 
of tests in Fig. 97 is here presented; as comparing performance with 



2,5 ,HP 30 AT 15 400 30 R.RM. 35 




20 p m 15 30 r 

Fig. 96.; — Tests of 7, 10, and 14 by 6 in. Willans Central-valve, Single-acting 
Engine. Group I, low-pressure cylinder, simple; group II, intermediate and 
low-pressure, compound; group III, whole engine, triple expansion. Clear- 
ances, high to low, 0.125, 0.105, 0.058. Engine run with late cut-offs and small 
compression. The basal m.e.p. is referred to the large piston in every case, and 
K is per cubic foot of displacement by that piston. 

The tests here given are from the first report, Proc. Inst. C. E., Vol. 93, 1888, 
page 128. A second report, on tests with the engine run condensing, is published 
in Vol. 114, 1893, but data for an investigation of the missing steam quantity 
were not included in the matter printed. 

and without jackets, this diagram might be placed in § 27 (e) or (/). 
Here we note that the lower values of the missing steam quantity agree 
well with the formula, Eq. (126); and that with the help of the jackets 
the engines are able, to carry low loads, about one-fourth of their rating 
with but little increase in the steam per horse-power-hour. The rela- 
tively high values of K mc , as also of steam consumed, indicate leakage 
from or past the high-pressure cylinder; Engine B is the worst in this 
respect, and A comes next. 

(g) The Influence of Cut-off. — This appears to be very fairly 
represented, in its effect upon the ratio m, by the use of Ve as a divisor 
in Eq. (126). As regards the actual quantity K mc , directly proportional 
to the missing steam at cut-off per revolution, the tests exhibited show 
that this changes very little with cut-off, keeping nearly constant over 
the range of ordinary working of the engine. It generally seems to 



186 



ACTION OF THE STEAM IN THE ENGINE 



[Chap. V. 



fall off a little with very short admission; and at the other end of the 
range, with very late cut-off, a more rapid decrease occurs, at least 
according to Figs. 87, 88, and 91. The last point cannot be considered 
as fully established, since some of the evidence is contradictory. 

As would naturally be expected, the ree vapor at ed steam increases 
steadily in amount with shorter cut-off and longer expansion. Figs. 
95 and 97 show how this action is strengthened by the steam jacket. 



0.04 




5 M.e.p. 10 Ref'd. 15 



Fig. 97. — Tests of Large Vertical, Compound, Four-valve Generator Engines, made 
with and without jackets and reheater in action; tests under service conditions, 
but with load held steady in each case. Nominal gage pressure at throttle, 
engines A to F, 160 lb., engines G to K, 135 lb. Scheme of diagram, same as 
in Fig. 88. Report by L. S. Marks, Trans. A.S.M.E., Vol. 25, 1904, page 443. 

(h) Effect of Theottling. — Taking throttling to mean the cut- 
ting down of the initial pressure by a throttle valve in order to con- 
trol the power of the engine, it is a subject which for detailed analysis, 
if that were worth while, would come later — this because it involves 
change in quality of entering steam and in range of pressure — but 
considered only as to general effect it appropriately follows the discussion 
of cut-off. Fig. 98 shows how initial condensation is diminished and 
finally abolished by throttling; deducting the clearance steam in test 
35, the expansion curve would just about agree with the saturation line. 
As to whether throttling is economical, compare test 31 in Fig. 90 with 
test 35 here. There the m.e.p. is reduced to 11.7 lb. and the output 
per pound is 63.6 B.t.u.; here, with reduction to 13.2 lb., AU has been 
cut down to 46.0 B.t.u. The conclusion is obvious; but while strong 



§ 22 (h)] 



EFFECT OF THE CYLINDER WALLS. 



187 



throttling results in decided loss, through the throwing away of so 
much available work, there is every reason to believe that moderate 
throttling is advantageous in combination with early cut-off for very 
light loads. 

Throttling as a means of control has its proper place in locomotives, 
and in other engines which must start frequently and under load. 
Even with a duplex quarter-crank engine, the cut-off must be late if 
the engine is to be able to start from any position. Under ordinary 
conditions, the locomotive has not enough " adhesion," or friction be- 
tween wheels and rails, to resist the turning effect of full steam pressure 
upon the pistons throughout their stroke ; consequently, some throttling 
is necessary, to prevent the wheels from letting go and slipping freely. 
In general, from a mechanical viewpoint, a nearly uniform driving 
pressure, such as appears in diagram 34, Fig. 98, is better at low speed 
than the kind of pressure variation that comes from early cut-off. As 
a method of governing stationary engines, throttling is justified only 
when simplicity and low first cost of the machine outweigh economy of 
fuel as determining considerations. 




Fig. 98. — Unit Diagrams from Engine 
of Figs. 87 and 90, showing effect 
of throttling. Test 1 from Fig. 90; 
in tests 33, 34, and 35, cut-off is at 
0.875 of the stroke. 



100- 




50- 



Fig. 99. — Diagrams from Engine of 
Figs. 87 and 90, showing effect of 
speed. 



(i) Effect of Speed. — This is strikingly shown in Fig. 99, with 
speeds in the ratio of 10 to 1. The valve action is the same in both 
cases, but at the low speed much more steam is admitted and a fuller 
diagram and higher m.e.p. are obtained, as appears at a. The unit 



188 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



diagrams at b show, however, that the initial condensation is far greater 
at the low speed, and the effective output per pound of steam is much 
less. Hyperbolas are drawn along the expansion curves, originating at 
cut-off, and the difference in reevaporation is thus clearly shown up. 

(j) Speed and Cylinder Action. — Figs. 100 and 101 are given 
to show how the__missing quantity varies with speed, and to test the 
correctness of ^/N as a term in the condensation formula. The quan- 
tities plotted at a are K mc and K mT , with K m f also in Fig. 101 ; the last 
is not marked off directly in Fig. 100, because of the crowding of the 
points. In Fig. 100 the steam pressure is about uniform, but there is 



1.4 














2 

Q— 




























\2 


\ 








b 




1 


>- 






J& 22 


3o- 






^17 




8 






1.0 


<2S% 


20i 

-°iT 






I0Jj~9 




+ 






•s 12 


ll 






I9h: 


^>I6 




15 










Cut-off Ranges. 
°- Late 0.47 to 0.54 
medium 0.21 to 0.27 
-0 Early 0.11 to 0.15 










0.06 

0.04 
Km 
0.02 


' i 


S 










- \ 


HP 


















- a 


4] 


£ 






ft 




a 










■i 






l m 


f 


P 







R.P 


M. 2 


* 


J 4 





6 





8 





100 



Fig. 100. — Variation of the Missing Steam Quantity with Speed. Same engine as 
in Figs. 86, 87, 90, and 99. At a, the missing quantity Km) at b the ratio 
r = mi/mc, of value by Eq. (126) to observed value at cut-off. 



a wide range of cut-off : note how the vertical lines connecting the two 
points, which show the amount of reevaporation, increase in length 
with earlier cut-off, as well as with lower speed. In Fig. 101 the formula 
runs high, especially with the higher initial pressure, but follows very 
well the trend of K mc . 

To test the speed function in Eq. (126), the ratio r = w f /m c is also 
plotted. In Fig. 100, individual values are given, and of course show 
a good deal of irregularity. By averaging in five groups and indicating 
the means by + marks, a better basis of judgment is established. For 
the group near 60 r.p.m., two mean values are shown, the higher got by 
including tests 1 and 2, in which r runs high for causes other than the 






§ 22 (j)] 



EFFECT OF THE CYLINDER WALLS. 



189 



speed — see Fig. 87. The mean point s_are so nearly on a horizontal 
line as to confirm strongly the use of ViV. 

In Fig. 101, means of r for the five groups are plotted near the base 
line. Here it appears that N ought to have an exponent a little greater 
than J: with a larger value, so that the divisor would be somewhere 



0.06 






i 

i 






Initial Pressure, Absolute. 

^ 121 LB. *i 104 LB. 




<*■ 


ft 




L 
1 

1 

1 


fit 84 


LB. s 


>t 64 


LB. 


0.04 
0j02 




a 


!' ' 
ii i 

1 • i 
1 • 


> 

x> 
J. 


!> 

If 




% 




' 






i 

i 


1 
1 
1 
1 

1 

J. 


i 
i 
i 

i 


o 


i 

i f- 


a 








6 


* 


? 


ho 




















V 




4 












b 
















o — 




j — 













R.F 


>.m. ^ 





4 





6 





8 






1.2 



1.0 



Fig. 101. — Speed Tests of 9 by 36 in. Corliss Engine, the same as in Fig. 95: tests 
at page 938 of reference there given. Engine run condensing, exhaust pressure 
2.3 to 4.3 lb. abs. in cylinder; cut-off constant at 0.4 of stroke; initial pressure 
at four different values, as indicated on diagram. 

between ^/N and ViV, higher speed would exert a stronger influence, 
and keep mi from increasing too rapidly. 

(k) Range of Temperature. — As implied in Art. (c), the amount 
of initial condensation is not in a simple proportional relation to the 
range of steam temperature within the cylinder. For presenting data 
along this line, and at the same time testing the sufficiency of the arti- 
ficial temperature function T in meeting observed conditions, the scheme 
of Fig. 102 is effective. The ordinate is the ratio r = mf/m c , as used 
in the last two figures, and the base is absolute steam pressure. For any 
test or group of tests averaged together, the line 12 has its height fixed 
by r and is determined horizontally by the range of pressure within 
the cylinder, from initial pi to p 2 during exhaust. If r runs high, the 
formula is too strong and should be weakened, and vice versa. 

From Mr. G. H. Barms' book of Engine Tests, Fig. 102 represents 
a combination of all the results from engines of the Corliss class which 
were " tight" or " fairly tight" against leakage when inspected stand- 
ing after the manner described in Art. (p). As would be expected in 



190 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



tests made under a variety of plant conditions, the points scatter pretty 
widely on a plot of individual values, r ranging from 0.78 to 1.35 for 



1.1- 
1.0- 
r- 

0.8- 



2 2. 



i — \ — t — i — r 
P 50 



i — r 



■j— r 



100 



150 



Fig. 102. — Ratio of Formula Value to Observed Value of the Missing Quantity, 
referred to the range of pressure within the cylinder. Tests of Corliss and 
equivalent engines, without jackets, in Barms' Engine Tests. 

A. Simple condensing engines, nine tests. 

B. Simple noncondensing engines, ten tests. 

C. Compound engine, high-pressure cylinder, nine tests. 

the whole group. The use of mean values is proper with such data, in 
that it tends to balance errors and erratic variations and bring out any 
underlying trend. So far as simple engines are concerned, the formula 
averages up very well, running just a little high, as it does also with 
the engine of Figs. 86, 87, etc. For the compound engines, m f at high- 
pressure cut-off does not work out big enough, in spite of the increase 
in range effected by substituting T from Table 10 for the actual tempera- 
ture t — the amount of the change being shown in the following tabu- 
lation, made for the average pressures in Fig. 102: 



k - 


Ih 


t 


T x 


- T 2 = 


316 


144 


172 


315 


184 


320 


220 


100 


321 


214 


351 


260 


91 


361 


246 



T 



Group A 
Group B 
Group C 



131 
107 
115 



A similar plot of mean results from six of the locomotives tested in 
the Pennsylvania Railroad Company's Testing Plant at the St. Louis 
Exposition of 1904 is given in Fig. 103. This involves the work-up of 
indicated steam consumption from the numerical data in the published 
book of reports: here engine No. 4 is omitted because it seems to show 
excessive leakage, No. 7 because superheated steam was used. The 
same general trend is evident as in Fig. 102, the shortening of the range 
of pressure and temperature exerting too much influence in the formula. 
Leakage is probably in large degree responsible for the very low value 
of r in cases 6 and 8. In getting this ratio, the factor m from Eq. (126) 
is applied to the total steam in the cylinder, including clearance steam, 
and the resulting missing quantity is divided by the actual (K — Kj c ). 

That data along this line are likely to be contradictory is well illus- 
trated by Fig. 104. The series of points lettered A**B shows mean 



§ 22 (k)] 



EFFECT OF THE CYLINDER WALLS. 



191 



values of the ratio r from the four groups of tests in Fig. 101, where a 
simple condensing engine was run with the initial pressure at about 
121, 104, 84, and 64 lb. abs.: each set of variable-speed tests at a par- 
ticular pressure is averaged together. It appears that the formula gives 
too much weight to the longer range of pressure and temperature, not 



r - 
0.8- 

0.6- 



B 1 " 



"i — I — r 
50 



T 1 1 1 1 1 1 1 

100 150 



-| 1 1 r 



200 



Fig. 103 



1. 

2. 
3. 
4. 
5. 
6. 
7. 



Ratio Diagram, Pennsylvania Railroad Locomotive Tests of 1904: see 
Figs. 105, 132, 133, 134. Engine sizes as follows: 
Simple, two-cylinder, 22 by 28 in., freight service. 
Simple, two-cylinder, 21 by 30 in., freight service. 
Compound, two cylinder, 23 and 35 by 32 in., freight. 
Compound, four-cyl. tandem, 19 and 32 by 32 in., freight. 

r 

Compound, four-cyl- 
inder "balanced," 
express service, 



fl4.2 and 23.7 by 26.3 in. 

1 Pi onrl OK K,r 9fi 4n 



15 and 25 by 26 in 
14.2 and 22.1 by 23.6 in. 
15.5 and 26 by 26 in. 



enough to the shorter, which is in accord with the showing of Figs. 
102 and 103. On the other hand, the three points S, C, and T repre- 
sent results from the same engine, when run simple and condensing, 
and when serving as the first cylinder in a compound and in a triple- 
expansion: the first group is diagrammed in Fig. 95, but for present pur- 
poses only tests without the steam jacket are used, and those at very 



1.2- 
r - 

1.0 



0.8 



B 



1 I I I r r 
P 50 



i — i — | — i — i — r 
100 



150 



Fig. 104. — Ratio Diagram, 9 by 36 in. Corliss Engine at Sibley College, 

also in Figs. 95 and 101. 

early cut-offs are omitted. These three group-averages have no very 
definite trend away from Eq. (126) ; and in this they agree with results 
from the 17 by 30 noncondensing engine of Fig. 86, etc. With the 
latter, tests were run at 60 and at 30 lb.' gage pressure, in addition to 
the main body of tests at 90 lb. by gage; and for these Eq. (126) keeps 
m f in very good alignment with m c . 

It is of interest to compare two of the engines just cited, in regard 



192 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

to the variation of m c with initial pressure. That of Fig. 104, in the 
A**B series of tests, makes m c increase as the steam pressure is lowered; 
in other words, the walls condense a larger fraction of the smaller 
weight of steam that comes in when the pressure and density are low 
even though the absolute weight condensed is less than at high pressure. 
In the noncondensing engine of Fig. 86, which agrees with Eq. (126), 
ra c keeps practically constant with changing initial pressure. 

(I) Influence of Temperature Range. — Reasoning from the in- 
formation just presented, and anticipating some of that set forth in 
§ 25, this matter may be put into the following fairly rational shape: 

In the working of the engine between the pressure limits p\ and p 2 , 
a cyclical variation of steam temperature through the range t = h — t 2 
is set up within the cylinder; and from this results the cyclical absorption 
and rejection of heat by the metal surfaces. 

If these surfaces followed the steam in temperature, either exactly 
or with a fair degree of proportionality, the amount of steam initially 
condensed would be proportional to the range t, or to some simple 
mathematical function of t, such as the square root. This hypothesis 
is not supported by the facts. 

Experimental measurements of the temperature cycle of the cylin- 
der walls — see § 25 — have shown that the temperature range of the 
surfaces is much smaller than that of the steam, and that the mean 
temperature of the metal is a good deal above a time-base mean of the 
steam temperature. This condition can be accounted for by the very 
reasonable assumption that there is a greater freedom of heat transfer 
from dense high-pressure steam to the metal than from the metal to 
the low-pressure steam of late expansion and of exhaust — see fuller 
statement in § 25 (j). 

The state of affairs shown in Figs. 102 and 103 will be made rational 
by the hypothesis that, as the pressure limits p\ and p 2 are changed, 
the range of wall temperature does not remain in constant ratio to the 
range of steam temperature, but varies at a less rapid rate. In other 
words, a moderate range of p and t, as from initial pressure to receiver 
pressure in the first cylinder of a compound engine, may set up a wall 
cycle of relatively high intensity: but an increase of steam range, as by 
dropping to atmospheric exhaust from this cylinder, will add very little 
to the amount of heat taken up and rejected by the cylinder walls. 

The change from the actual range of t to that of the quantity T in 
Table 10 is a purely empirical attempt to meet existing conditions; and 
this function T has been chosen, after trial, in preference to the obvious 
scheme of damping the influence of t by adding a constant, or of using 
(t + C) in the condensation formula. As between condensing and non- 






§ 22 (I)] EFFECT OF THE CYLINDER WALLS. 193 

condensing simple engines, T seems to meet requirements quite suc- 
cessfully; for high-pressure cylinders the other expression, perhaps 
(t + 100), might be better. It will not do to make the T-curve in Fig. 
89 rise more steeply at high pressures, for that would give the tempera- 
ture range entirely too strong an influence in an engine with a very 
long pressure range, such as the simple locomotive in Fig. 105. The 
practical expedient is to change the coefficient C, fixing different 
values for particular conditions: thus if Fig. 102 is truly typical, C 
should be made about 0.31 for compound engines of the class repre- 
sented. Only by such adjustment can class peculiarities be taken into 
account; and the essential prerequisite is a good body of data from 
engines of the class under consideration. 

(m) Engines with Lakge Compression. — This class is well rep- 
resented by the locomotive, with the Pennsylvania Railroad tests of 
1904, already instanced in Fig. 103, offering a large body of very com- 
plete data. Four sets out of the eight are plotted in Fig. 105, accord- 
ing to a scheme especially useful in the case of compound engines, for 
which that of Fig. 87 would become confusing. The diagram is based 
on the quality curves FF and GG in Fig. 82, but only at the " critical " 
cut-off and release points is the condition of the steam shown. The 
ordinate is absolute pressure, the abscissa the -fraction of the working 
steam, or of the steam supplied to the cylinder, which is accounted for 
by the indicator. The clearance steam is not included in this ratio, so 
that mi, indicated by cross-marks at cut-off, does not come directly 
from Eq. (126) with this class of engines, but must be worked out by 
the method described under Fig. 103: that is, the total steam is multi- 
plied by m from the formula, then the resulting K mi is divided by the 
admitted steam K. The experimental points belonging to a particular 
test are strung together by a broken line, but the segments of this line 
have no physical meaning. 

For Fig. 105, the tests at the same speed are averaged together, so 
that in most cases a group of three to five tests is represented. Point 
A shows the pressure in the steam pipe and the practically unit quality 
of the steam coming to the engine. On the pressure line at cut-off B, 
a cross-mark shows the formula value, obtained as just described. On 
the line from high-pressure release C to low-pressure cut-off D, a cross- 
mark F indicates the lowest exhaust pressure in the high cylinder; for 
the simple engine No. 2, F is the exhaust pressure in the single cylinder. 
From D to E are shown the range of pressure and any change of quality 
during low-pressure expansion. 

The actual size of the missing fraction m is more valuable informa- 
tion than the ratio borne to it by the mi from an arbitrary formula, so 



194 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



that Fig. 105 is a much more useful type of diagram than the preceding 
figures. For purposes of comparison, one simple engine is included; 
and the most striking thing brought out is the small gain in quality at 
cut-off that is realized from compounding. Engine No. 3 shows an 
advantage of from 3 to 10 per cent over No. 2, but in Nos. 5 and 6 the 
missing quantity is fully as large as in the simple engine. 



0.4 


0.2 m C 


200- 


I 


k r-^/ 






B< 


$// 




- 




U° 




150- 








100- 








- 


c 1 


1 




P " 




1 




50- 




NC 


).2 


Lb.- 








Abs.- 


F + 


f + 




n 


j 







04 
A 



0.2 m 





r + 

I r 


r 


< 


\jl 




F 


f D 






Ie ^ 


Jo. 3 



0.2 rrx Q 




0.2 m Q 




^0.6 0.8 x |.0 0.6 0.8 * 1.0 0.6 08 * 1.0 0.6 0.8 x \0 

Fig. 105. — Quality Diagrams, for four of the locomotives listed under Fig. 103. 

The basis of representation is partly responsible for the apparent 
failure of the missing steam to decrease as the range of pressure in the 
cylinder is made less by compounding: if the total steam were the base, 



Data from 


Locomotives Represented 


in Figs. 


103 AND 105. 


Engine 


i 


2 


3 


5 


6 


8 


Clearance 


0.113 

0.42 

0.12 


0.093 

0.54 

0.07 


0.167 

0.70 

0.23 


0.133 

0.68 

0.21 


0.183 

0.64 

0.26 


0.169 


K c ( maximum 


0.74 


K \ minimum 


0.27 



As regards the grouping in Fig. 105, it is to be noted that the ratio KJK will 
be higher as the speed increases, because the average cut-off is earlier at higher speed. 

m would be smaller and would vary more. The clearance steam in the 
high-pressure cylinder has relative values of the kind shown in the 
tabulation just given, where K c stands for clearance steam, calculated 
as if dry saturated at the beginning of compression, while K is the 



§ 22 (m)] EFFECT OF THE CYLINDER WALLS. 195 

admitted working steam by feed-water measurement: the ratio is a 
good deal larger in the compounds. The uneconomical effect of ex- 
cessive compression, more fully discussed in § 23, is strikingly apparent 
in these tests. Indicator diagrams from engines 2, 3, and 5 will be 
found in Figs. 132 to 134. 

The marked discrepancy between formula and experiment is a strong 
indication of leakage, and a number of incidental inferences confirm this 
suggestion. Thus in engine No. 3, m increases from cut-off to release 
in the high-pressure cylinder (as against a normal decrease through re- 
evaporation), which would be accounted for by exhaust leakage, from 
the cylinder to the receiver; again, the quality in the low-pressure 
cylinder is almost independent of the speed, which is reasonable if rel- 
atively greater leakage at low speed balances increased cylinder-wall 
action. In No. 5 there is an anomalous increase of m with speed at 
240 and 280 r.p.m., due perhaps to the development of some defect in 
the valves or in the piston packing as the tests proceeded ;, at 280 
r.p.m. but one test was made, so that the apparent result lacks con- 
firmation. With engine No. 6, the large size of the missing quantity 
seems to indicate copious leakage; but the fact that m varies so much 
with the speed in the low cylinder implies that this is valve leakage, — 
from live-steam supply right through to exhaust, — and the type of 
construction, with a single piston valve for the two cylinders together, 
rather favors this idea. 

As regards the effect of speed, actual m c and computed 7Wf keep in 
fairly constant ratio in each diagram, except for the marked discrepancy 
in No. 5, already alluded to, and a smaller divergence of the same sort 
in No. 2. The close similarity in the manner of variation of the two 
quantities in No. 6 weakens the hypothesis of excessive leakage, since 
that would exert a relatively greater effect at low speed, as appears in 
the high-pressure cylinder in No. 3. 

(n) Influence of Size. — Direct experimental data upon this 
point, in the way of exactly similar tests upon exactly similar engines of 
different sizes, do not exist, and would be extremely difficult to secure: 
only by trial and inference can the correctness of the expression incorpo- 
rated into Eq. (126) be judged. In apparently serving equally well for 
the small engines of Figs. 93 and 96 and for the large ones of Figs. 91, 
94, and 97, the ratio s seems to meet the situation very fairly. Obvi- 
ously, there must be some class variation, due to differences in arrange- 
ment of valves and ports and in the relative amounts of clearance sur- 
face. This can be found only by trial calculation, from the results of 
numerous tests, and will then be combined with the size factor, or else 
make itself evident in the "constant" C. 



196 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



The condition of the surfaces must have some influence upon the 
freedom of heat transfer, although probably not a great deal. Polish- 
ing the faces of piston and cylinder head has been tried as an expedient 
for diminishing cylinder action, but not with any striking result. 

(o) Value of the Condensation Formula. — The useful applica- 
tions of this formulation of test results have been named in Art. (d) : 
by giving a probable value of the missing quantity, it makes the engine 
an approximate steam meter, with data from indicator diagrams alone; 



0.25 



0.20- 



0.15- 



0.10 




0.05- 



0.05 



34 M.E.R 35 



Fig. 106. — Callender and Nicholson Tests, Proc. Inst. C. E., 1897, Vol. 131. 
Engine 10.5 by 12 in., normal speed 250 r.p.m., clearance 0.10; shaft governor, 
valve as in Fig. 259. During experiments, governor was disconnected, eccen- 
tric clamped so as to give cut-off at about 0.2 of stroke, and speed was regu- 
lated (by a brake load, presumably) at the values marked along the ordinate 
lines, from 44 to 97 r.p.m.; engine was made single-acting by fastening to the 
valve an extension which kept the crank-end port always covered. Steam pres- 
sure 90 lb. by gage, exhaust atmospheric, into surface condenser. 

and it serves as a check upon steam-consumption tests of working 
plants, referring especially to tests of the less precise type, such as are 
often the best that can be made under actual plant conditions. 

In the great body of experiments upon which the formula is based, 
fairly represented by the examples which have been given, there must 
be considerable variation in quality of data. It is safe to say that in 
the best engine test that can be made there is, in the final relation of 
steam consumed to power developed, a possible error of 2 or 3 per 
cent; while under ordinary plant conditions, the uncertainty, even 
with reasonable care, may easily lie in the range from 5 to 10 per cent. 



§ 22 (o)] EFFECT OF THE CYLINDER WALLS. 197 

Beside this possible error, there is reason to believe that some of the 
influences affecting the steam action are likely to fall into a state of 
rather unstable equilibrium, so that a slight preponderance or impetus 
in one direction will produce an erratic effect — witness the fact that it 
is found necessary to run the more complex engines for quite a time be- 
fore beginning a test, in order to establish steady conditions and get 
consistent results. 

Considering these uncertainties in the data, with the number and 
complexity of the influences which contribute to the net performance of 
the engine, too much must not be expected in the way of an accurate 
prediction. An estimate of actual steam would be made by dividing 
the indicated steam (at cut-off) by the fraction (1 — m f ), having com- 
puted ra f through Eq. (126). Certainly, if the measured consumption 
differs from this estimate by more than 5 per cent on the side of deficiency 
or of 10 per cent on the side of excess, there is strong reason to ques- 
tion the accuracy of the test, or, in the case of excess, to feel assured 
that leakage is active. In engines with small compression, there will 
generally be better agreement than this ; but with those having single slide 
valves and large compression, the net action seems to be more indetermi- 
nate and irregular, and is certainly more likely to be modified by leakage. 

(p) Leakage. — The ordinary test for leakage consists in setting or 
blocking the engine in various positions and seeing whether steam es- 
capes. With a slide valve, the wheel is turned until the eccentric radius 
stands about perpendicular to the stroke line, making the valve cover 
both ports, and the throttle valve is opened; separate admission valves 
can usually be released and moved into the closed position by hand. 
The indicator cocks may be used to see whether steam is getting into 
the cylinder, although it is better to take off the back head and get a 
clearer view, of one end at least: escape directly to the exhaust should 
also be looked for, with a single valve. Leakage past the piston and 
from the cylinder to exhaust is detected by blocking the wheel or crank 
and turning steam into one end of the cylinder. The dead center is 
the easiest position in which to hold the piston against steam force, and 
is sufficient for the test of the valve: but the piston should be tried at 
several points along the stroke line, if it can be properly held. 

Of quantitative tests, with measurement of the amount of leakage, 
comparatively few are on record. Probably the most striking example 
is that diagrammed in Fig. 106. The main purpose of the experiments 
was the measurement of temperature, in metal walls and in steam — 
see § 25 (c) — but only the leakage determinations will be discussed at 
this point. 

The diagram in Fig. 106 is plotted on the system of Fig. 87, with the 



198 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

steam K per cubic foot of piston displacement as ordinate and . the 
mean effective pressure as base, so that all the quantities are shown 
also in pounds per horse-power-hour. The various amounts of steam 
laid out are as follows: 

Measured from the base line MM, which is placed at the zero of 
the vertical scale, MA is the actual steam supplied, as condensed and 
weighed : MB is the steam actually kept in the cylinder for useful effect, 
deduced by subtracting the amount AB of leakage, as found by sepa- 
rate experiment. This leakage was chiefly past the long sides of the 
valve (not the ends, which cover the ports), directly from steam chest 
to exhaust: it was nearly constant per unit of time, hence the rate per 
unit of displacement varies rapidly with the speed of the engine, in 
inverse ratio. The valve was found to be practically tight when sub- 
jected to the standing test just described above, and the high rate of 
leakage was attributed to the breaking up of the oil film by motion; 
the steam was supposed to escape largely in the form of water, formed 
by condensation on the relatively cool edges of the exhaust port or 
chamber. 

To return to the diagram, MC is the indicated clearance steam, 
c/s c in Eq. (117), taken to be the actual weight, under the assumption 
that this steam is about dry at the beginning of compression; and CD 
is the gross indicated steam at cut-off, or e/s e , so that MD represents 
the net indicated steam, K K \ ME, shown for test 1 only, is the net 
indicated steam at release, or Ki T . From their temperature results the 
experimenters calculated the probable amount of steam actually con- 
densed by the walls, which was of the- same order of magnitude as the 
quantity DB. 

To bring our missing-quantity formula into the discussion, the total 
indicated steam at cut-off, CD in Fig. 106, has been divided by (1 — TWf) 
as got from Eq. (126); the result is laid off as CF, so that MF is the 
estimated steam consumption, to be compared with measured MB. If 
the indicated steam MD remained at about 20 lb. per h.p.h. when the 
engine was raised to the speed of 250 r.p.m., the consequent change in 
rrii would reduce the estimated consumption to about 28 lb., which 
would be very good performance for an engine of this size and class. 

In these experiments, the valve leakage, already quoted as the 
principal component, was determined by plugging the steam ports 
with lead and running the engine with a motor, full steam being turned 
on at the throttle valve. Very nearly, the rate of escape, inferred to be 
mostly in the form of water, was found to vary directly as the perim- 
eter of the valve and inversely as the width of overlap; and similar 
tests of other valves gave concordant results. With the ports open, the 



§ 22 (p) EFFECT OF THE CYLINDER WALLS. 199 

ends of the valve partly ceased to be available for leakage from live- 
steam to exhaust space; and uncertainty on this score raises a doubt as 
to the validity of the allowance which determines net steam MB from 
total condensed steam MA, as laid out in Fig. 106. In engines with 
separate steam and exhaust valves, this direct leakage to exhaust is 
impossible: and Eq. (126) is so largely based upon the performance of 
engines of the latter class that it probably covers but a small rate of 
leakage. In this connection, refer back to the remarks about leakage 
in Art. (m), under Fig. 105. 

In general, leakage is something that can hardly be made predictable 
from determinate controlling conditions. The idea that it may assume 
considerable magnitude, even when the engine appears tight in a static 
inspection, has an important bearing upon the validity and usefulness 
of the method of thermal analysis described in § 24. 

§ 23. Effects of Compression 

(a) Action of the Cleakance Steam. — If the steam in the cylinder 
was of the same average quality during expansion and compression, 
the curves of the two operations being essentially similar in form, the 
wasteful effect of clearance could be almost completely neutralized by 
compression. Turning back to the Rankine cycle, § 15 (d), we can 
readily see that a body of clearance steam might be so handled as not 
to affect the unit output or the efficiency of the cycle. This steam 
would be trapped in the cylinder at the end of exhaust and, further, 
would have just enough heat abstracted from it at the lower temperature 
£2 to make adiabatic compression bring it to the state of the entering 
steam.* Then in expansion the clearance steam would perform all the 
work received in its compression, and with complete expansion its net 
work effect would be zero. Such a similarity of the two operations 
cannot be realized in the actual engine, so that the loss of available 
work which necessarily results from the presence of clearance can in 
but a small degree be diminished by compression. 

As already briefly suggested in § 19 (k), the clearance steam (as a 
part of the whole body of steam in the cylinder) has a lower quality 
during expansion than during compression, hence does less work than 
it receives, causing a net loss. Using for illustrative purposes a steam 
diagram of actual form, the ideas set forth in § 19 (g) to (k) will now r be 
worked out to a definite conclusion, which will show the best possible 
or imaginable result from the use of compression. The modification 

* This would not be the same as the adiabatic compression of the whole charge 
in the Carnot cycle. . 



200 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



by wall action will then be introduced, leading to the true relation, 
which is amply confirmed by experiment. 

(b) The First Assumption. — In Fig. 107, with a constant ad- 
mission and expansion line ABCD, the back-pressure line DEF is varied 



J GA 



H s 



100- 




Fig. 107. — Steam Diagram with Variable Compression. 

by changing the amount of compression, with equal increments, from 
zero to enough to raise the terminal point F up to the initial pressure 
at A: for convenience, curves BC and EF are of the form pv = C. The 
diagram is drawn to scale for one pound of total steam expanding, the 
full volume of which would run out to the saturation line SS; and at 
cut-off B the quality of the whole steam in the cylinder is 0.75. 

. At first we ignore SS and disregard initial condensation. After ex- 
tending curves CB and EF up to the line JH, the length GH is taken 
to represent the volume (and weight) of the steam admitted from the 
boiler: division of each HG by the full one-pound volume JS gives the 
weight of this apparent or indicated working steam which corresponds 
to each of the five degrees of compression. 

By a method described under Fig. 114 and in § 32 (g), an area scale 
of so many B.t.u. to the square inch can be calculated for the diagram 
in Fig. 107; then from planimeter measurements of the several ABCDEF 
areas, the cycle output AU (as in Fig. 90, etc.) is found for each case. 
Division of this A U by the weight found from GH gives the output per 
pound of steam admitted, expressed in heat units. In Fig. 108 the 
curve AB is laid out with this latter quantity as ordinate, the base 
QE being the same as QE in Fig. 107, so that the abscissa is the length 
along the stroke line, or the volume, through which compression takes 
place. The maximum of the curve, located graphically at M, shows 
the best degree of compression under the assumption which governs 
the determination. 



§ 23 (&)] 



EFFECTS OF COMPRESSION. 



201 




N 



liuj^innjjjj; 



ifflMI 



Q 



To cover the case of no clearance, area JABCDP is similarly com- 
pared with the steam of volume JH: the resulting unit output fixes the 
height of line CD. A vertical in- 
tercept between CD and AB shows the 150- 
loss due to clearance. For this first 
assumption, if the expansion was com- 
plete, curve BC (Fig. 107) continuing 
without change of form until it met , 00~ J ' 
line PD, curve AB (Fig. 108) would 
have its maximum at B, and would AU . 
there touch the line CD, showing com- 
plete neutralization of clearance waste. 5° 

(c) Real Character of the 
Compression Effect. — Now go 
back to Fig. 107 and take into ac- 
count the important fact that at cut- ° 
off — whether actual at B or effective Fig. 108. — Curves of Performance, for 
at H — the steam in the cylinder has ideal and actual condition s. 

some fractional quality x h here 0.75. Assume that the clearance steam 
is dry saturated at E, so that its true weight can be calculated from 
the volume PE. Carry the several clearance-steam weights up to the 
line JS, laying off the corresponding full volumes in the lengths JG 
on the enlarged diagram at a. Also, multiply these JG volumes by X\ 
and get JG', which shows the clearance steam as of the same quality as 
the total steam at H. Note that these points are entirely independent 
of the form of the compression curves, which in its detail is an uncertain 
matter, determinable only by experiment, and unknowable in the ex- 
tension FG dotted in upon the main figure. The length JG' represents 
the effective service of the clearance steam, in filling space that would 
otherwise have to be filled with fresh steam from the boiler. 

To get what will be a very close approximation to actual perform- 
ance, we keep the AU values found from the areas ABCDEF, but use 
the new values of the steam weights which are represented at a. As a 
first step from the curve AB in Fig. 108, the true weights of the ap- 
parent working steam are found from the volumes G'H; and with these 
weights as divisors the curve A'B' is obtained. Note the decided 
diminution in the amount of desirable compression, as determined 
by the maximum M', also how much greater loss will be caused 
by excessive compression. The final curve FG is similar to ATT, 
but is based on the real steam weight, volume SG in Fig. 107a, in- 
stead of the indicated steam: the same AU values are divided by the 
weights from SG and SJ, giving the ordinates of the curve FG, in 



202 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



Fig. 108, and the height of the reference line HK for the case of no 
clearance. 

In effect, this is nothing but a comparison of indicated work with 
steam consumed. As Fig. 107 is laid out, two simplifying approxima- 
tions are incorporated into the discussion: the first, however, or the use 
of similar curves, is wholly a matter of convenience, and the method is 
equally available when the compression curves differ from the expan- 
sion curve and among themselves. Of much greater importance is the 
use of a single, unchanged expansion curve BC as related to the un- 
changeable SS line for the pound of total steam, since this involves the 
assumption that the initial condensation (and subsequent quality 
variation) of the whole steam is independent of the relative amount of 
clearance steam. Some experimental information upon the last point 
is now in order. 

(d) Behavior of the Compressed Steam. — This is strikingly 
shown in Fig. 109, by results from experiments in which the conditions 





~w\ 






80- 


fl\ \ 










r "\\M \ 






60- 




l \ V \ 

\\\ \ 






- 




H vA 






40- 




f w \ 






P- 


\4 x \ \ 








tf V 


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20- 






^^^^ 




E 


E 


\ i 







i, ib 




zb 



Fig. 109. — Unit Indicator Diagrams from Tests by Professor Dwelshauvers- 
Dery upon an 11.8 by 23.6 in. engine at the University of Liege. Revue de 
Mecanique, 1897, Vol. 1, page 939. Clearance 0.066, cut-off at 0.1 of stroke, 
compression through 0.1 and 0.4 of stroke: speed 61.7 r.p.m., saturated steam, 
atmospheric exhaust, no jackets. 

were intentionally so arranged as to exaggerate the effects of com- 
pression. The diagrams are laid out for one pound of total steam ex- 
panding, that is, of clearance steam plus admitted steam, and SS is the 
saturation line for the pound of steam, as in Fig. 107. Redrawn from 
rather small printed diagrams, those in Fig. 109 are not of high accuracy 
in the minor details, but the general form is reproduced with essential 
correctness. Later experiments on the same engine — see § 25 (i) — 
have shown that the clearance steam was superheated at the begin- 



§ 23 (d)] EFFECTS OF COMPRESSION. 203 

ning of compression, and throughout the greater part of that operation, 
which because of the consequent low rate of heat transfer was in large 
degree adiabatic. This is made apparent in test 6, by drawing a curve 
EH of constant steam weight — not greatly different from a curve of 
(moderate) uniform superheat — from the beginning of compression : 
the indicator curve rises decidedly above this reference curve until 
heat abstraction by the walls becomes active; while after condensation 
is established the compression curve droops so as to form a hook, show- 
ing a very rapid shrinkage of the product-measure pv. 

Expansion and compression curves of the relative form shown in 
test 6, Fig. 109, are often obtained from engines of the single-valve, 
shaft-governor type — see § 39 (g) — when running with a very light 
load or with only their own friction load, this valve gear giving long 
compression with very early cut-off. The peculiarities here evident in 
such exaggerated form represent influences which are always present, but 
which under ordinary conditions of working are scarcely strong enough 
to make their effects apparent. In many engines, the compression 
curves are hardly distinguishable from the equilateral hyperbola; and 
frequently, with large compression, there is merely a small decrease in 
the product pv toward the upper end of the curve, as a slight approach 
to the droop or hook here shown. It is to be noted that only when 
taken with a reducing motion of assured accuracy may the compression 
curve of a diagram be subjected to really close analysis. 

(e) Influence of Compression upon Expansion. — As bearing 
upon the question implied at the end of Art. (c), the two diagrams in 
Fig. 109 suggest the important practical conclusion that the condensa- 
tion factor m for the total steam is essentially independent of the amount 
of compression — this for the case of constant cut-off in the cylinder, 
with compression varied. Incidentally, the mark at M on Figs. 109 
and 111 shows the application of the factor mf, as computed from Eq. 
(126), to the total steam at cut-off. In further illustration, Fig. 110 
gives the results of the six experiments published, laid out on the com- 
pression base that is used in Fig. 108. The ordinate is steam per cubic 
foot of piston displacement, and the quantities plotted are as follows : 

AB is the total steam, made up of clearance steam AD and admitted 
steam DB: the weight of the former was computed as for dry satura- 
tion at the beginning of compression. The effect of speed is clearly 
shown in the difference between the two BB* lines. 

AC is the gross indicated steam at cut-off: its (small) variation from 
constancy shows that the cut-off was not kept quite uniform in effective 
value. 

CB is the total initial condensation, with the comparatively small 



204 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



variation just noted: the ratio m = CB/AB is more nearly constant 
than CB itself. 

AE is the indicated clearance steam at the end of compression, or 
at the point F in Fig. 109. The difference DE shows the condensation 
of the clearance steam by the cylinder walls before admission begins: 
it is really a part of the total condensation BC, although not so placed 
on the diagram. 




0.1 Comp. 0.2 



Fig. 110. — Steam-quantity Diagram of the Dwelshauvers-Dery compression tests. 
In tests 1, 2, 3, r.p.m. = 45, in 4, 5, 6, r.p.m. = 61. 

It would naturally be expected that with earlier compression the 
amount of steam condensed by the cylinder walls will increase, because 
the time during which the steam is above the temperature of the walls 
is made longer. This expectation is met in Fig. 110, but the increase 
is relatively small, not big enough to interfere with the usefulness of the 
assumption of constancy in approximate discussions. This assumption 
underlies the application of the factor m from Eq. (126) to the total 
steam in large-compression engines, as described in the definition in 
§ 22 (b) and exemplified in Figs. 103 and 105. In § 24 (c) it is shown 
that if the missing quantity at cut-off remains constant, there is implied 
a considerable increase, with compression, of the heat absorbed by the 
cylinder walls. 

(/) Cycle of the Clearance Steam. — Knowing the ratio of 
clearance steam to total steam, by weight; it is a simple matter to lay 
out the expansion curve of the quantity of steam that was compressed. 
For the two tests in Figs. 109 and 111, the value of this fraction, or of 
AD/AB in Fig. 110, is, respectively, 0.189 and 0.471. In Fig. Ill, any 
volume ac of the total steam is multiplied by the factor just given in 
order to get the volume ae of the clearance steam. 

It now appears that the clearance steam follows a complete cycle 
of its own: and since during compression the steam receives more work 



§ 23 (/)] 



EFFECTS OF COMPRESSION. 



205 



than it gives back during expansion, the cycle has a negative output, 
represented by the shaded area in each case of Fig. 111. With incom- 
plete compression, test 4, the manner in which the new steam con- 
tinues to compress the old steam, above F, is indeterminate; but since 
this action involves the kinetic loss explained in § 19 (i) and (j), it is 
proper to make the line FA serve as one of the boundaries of the lost 
area. 

Of the shrinkage in effective output due to the harmful influence of 
the cylinder walls, a portion bears upon the clearance steam, as shown 
by these cycle diagrams, and only the remainder is carried directly by 




v 10 20 

Fig. 111. — Cycle of the Clearance Steam, same diagrams as in Fig. 109. 

the new, working steam; but ultimately all the loss comes upon the 
latter, whence results the fall in efficiency which occurs when compression 
is increased beyond a moderate amount under a certain cut-off. In 
slightly different statement, the total missing quantity with diagrams 
like Figs. 107 or 109 is in a nearly constant ratio to the total steam; 
hence its ratio to the working steam will increase rapidly as the latter 
is made smaller through excessive compression. 

This is closely analogous to what takes place when cut-off is made 
earlier in a small-compression engine. As shown in § 22 (d) and (e), 
the steam condensed per revolution varies but little with cut-off, there- 
fore as the latter is made earlier the relative magnitude of the missing 
quantity increases. It has been suggested that an engine with large 
clearance might be governed, in part at least, by varying the com- 
pression instead of the cut-off. Which scheme would cause the greater 
loss of efficiency, in the reduction of the mean effective pressure to a 
desired small value, is a question that could be answered only by ex- 
periment, because secondary actions of unknown amount would vitiate 



206 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



conclusions drawn from approximate deductions by methods like that 
of Fig. 107. 

In terms of Fig. Ill, test 4, jhe gain from a moderate compression 
continues so long as area AKG decreases more rapidly than EFKH 
increases. ] 

(g) Tests with Variable Compression. — In Fig. 112 is plotted 
a set of tests made to determine the effect of compression upon economy. 
Here and in Fig. 113, the ordinate is steam consumption in pounds per 
horse-power-hour, in effect the reciprocal of the ordinate in Fig. 108, 
so that a minimum now shows best performance. In each series of 




Fig. 112. — Tests on 7.1 by 17.7 in. Corliss Engine, at Dresden, A. H. Klemperer, 
Zeitschrift des Vereines deutscher Ingenieure, 1905 I, page 797. 
Clearance 0.045, increased to 0.152 in series VIII; speed 101 to 102 r.p.m. 
Series I, II, VIII, steam at 100 lb. abs., condensing. 
Series III, IV, steam at 114 lb. abs., noncondensing. 
Series I, jackets on; others, no jackets. 

Series IV, superheat of 90 deg. fahr.; others, saturated steam with about 0.01 
of moisture. 

Fig. 112, the cut-off is held constant at the percentage of the stroke 
indicated by the number on the curve, and compression is varied. 
Between series I and II there is the difference in consumption due to 
the steam jackets (on heads and barrel), but the curves are very similar; 
in both cases, more compression is allowable with the later cut-off. 
Series III is the most complete, in that it contains tests with but 0.01 
of compression, and shows an unmistakable minimum of consumption 
at about 0.09, or at twice the clearance volume. Series IV agrees with 
III in form, and differs by what might be expected as to the gain from 
superheating in so small an engine. Curve VIII shows tests made 
after the clearance had been increased to more than three times the 









§ 23 (g)] 



EFFECTS OF COMPRESSION. 



207 



normal value; now the best performance comes with more than 0.3 of 
compression. 

The tests in Fig. 113, directly plotted at I, were made in series with 
constant compression and variable cut-off; here the numbers on the 
curves show the percentages of the stroke through which the steam is 
compressed. On the same base with I, lines relating m.e.p. to cut- 
off are plotted at II. From these two groups of curves are derived 
those at III, which relate consumption to compression when m.e.p. 
and i.h.p. are kept at a constant value. As an example, the horizontal 
line for m.e.p. = 30, in group II, cuts the m.e.p curve for 0.11 com- 



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c 


) Co 


MP. 0. 





0u 


>0 



Fig. 113. — Tests on a 9.8 by 19.7 in. Corliss Engine at the University of Ghent. 
Professor J. Boulvin, Revue de Mecanique, 1907, Vol. 20, page 109. 
Clearance 0.038, speed 101 to 103, steam pressure 93 lb. abs., non condensing; 
m.e.p. 24 to 33 lb., i.h.p. 18 to 25. 

Tests at I, II, and III, with jackets; curves aj IV derived from tests without 
jackets. 

pression at A, where the cut-off is about 0.168. Projecting A down to 
B, on the curve for the same degree of compression, we get the cor- 
responding steam rate S. The latter is carried over to III, where the 
ordinate is located on a base of compression percentage. These curves 
show how consumption varies with compression, but do not indicate 
coincident cut-offs, leaving these to be read off from I or II. The 
curves at IV are similar to group III, but represent another lot of tests, 
made without steam in the jackets. 

The primary curve 3 in group I is of such different form from the 



208 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



others as to appear somewhat doubtful, both in itself and in the very- 
high points which it determines at the left-hand ends of the curves in 
group III. Of greater interest is the shape of the latter curves to the 
right of their minima: the way in which they first rise rapidly, then 
more slowly, needs explanation. This can be given in terms of the 
statement under Fig. 112, that more compression is economically allow- 
able with later cut-off, which holds true until the incompleteness of 
expansion becomes considerable. With more compression there must 
be later cut-off for the same m.e.p.; then the condensation factor m is 
smaller, and the clearance steam is relatively less in amount. For a 
given compression, therefore, the negative work] as in Fig. 1 Ill Jis abso- 
lutely less and is deducted from the output of a larger weight of work- 
ing steam. 



100- 

80- 

60- 

40 
P 

20 





A 








V 


- 




1 
J 


E 95=P 






\ 324.2 =t 










(Mui 

a. 


3456 

Ft Lb 
4.443 

B.TU. 


3t 

CO* 






1.2 Cu.Fr 






- 










""^-■— — -_S 30=P 




250.3=f 


^N. 




_ 












D 


Q 








i 


i i 


i i 


1 1 l 1 i 


i i 





M F 5 v |0 

Fig. 114. — Data for Hirn's Analysis. 



N 



(h) Conclusions. — Merely for emphasis, the following conclusions, 
deduced in the course of this discussion, may be grouped together: 

Clearance always causes a loss of effect, which can in but a small 
degree be diminished by compression. 

Under any conditions, the introduction of some compression will 
be advantageous; but the best amount may be small, and is less as the 
conditions of working cause the initial-condensation fraction m to be 
greater. 

In the earlier ranges, as the cut-off is shorter the desirable com- 
pression is less. The converse, that compression may increase with 
cut-off, holds until incompleteness of expansion begins to exert an 
opposing influence; so that there will be some cut-off for which the 
economically allowable compression will have a maximum value. 

Taking Fig. 107 to be fairly typical in its proportions, we see that 



§ 24 (a)] ANALYSIS FOR THERMAL EFFECT. ' 209 

enough compression to meet mechanical requirements and promote 
smooth running — refer to § 34 (c) — even if it be in excess of the 
best amount from thermodynamical considerations, may be introduced 
with entailing appreciable or serious loss. 

§ 24. Analysis for Thermal Effect 

(a) Heat Added, Energy Change, and Work Done. — Take the 
fundamental statement of relation for a thermodynamic operation, 
Eq. (14), 

Q=I+AU, 

and modify its form by letting 7i stand for internal energy at the be- 
ginning and Ii for internal energy at the end of an operation, so that the 
energy-change I is equal to (7 2 — 7i). Also, repeat the definition of 
AU as the heat value of the external work done in the passage from 
state 1 to state 2, and of Q as the heat imparted from without. Then 

the equation 

Q = h-h + AU (130) 

furnishes a ready means of determining the amount of heat imparted 
to the steam in, say, the operation of expansion within the engine. An 
example will best illustrate principle and method. 

(6) Calculation from the Indicator Diagram. — In Fig. 114 
the volume scale is such that the diagram represents the performance 
of one pound of total steam. The clearance steam, taken to be dry at 
the beginning of compression at Q, is 0.206 of the total steam : then the 
diagram is for 0.794 lb. of working steam, and the clearance steam is 
0.206 -5- 0.794 or 0.26 of the working steam per cycle. At E the quality 
is Xi = 0.80, at S it is xi = 0.857. The two values of internal energy 
are first computed with data from Table II by Eq. (79), I = K — ml, 
as follows : 

7i = 1103.7 - 0.20 X 809.6 = 1103.7 - 161.9 = 941.8; 
h = 1087.1 - 0.143 X 868.4 = 1087.1 - 124.2 = 962.9: 
then (7 2 - h) = 21.1 B.t.u. 

By planimeter measurement, the work area ESTF is found to be 
equivalent to 75/3 B.t.u.: the dimensioned square, above the indicator 
diagram, represents one square inch on the original drawing, and shows 
how the area scale is derived from the linear units. Substituting in 
Eq. (130), we have 

Q = 21.1 + 75.3 = 96.4 B.t.u. 

This is per pound of total steam in the cylinder; per pound of working 
steam it would be 96.4 X 1.26 = 121.4 B.t.u. 



210 ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 

In this assumed diagram, smoother in outline than if actually taken 
by the indicator, the expansion is made to follow exactly the curve 
pv = C. It is of interest to note the decided increase of internal energy 
that takes place; the heat returned by the cylinder walls is not only 
sufficient in amount to equal the external work done, but there is a 
surplus left over to be added to the thermal energy of the steam. 

(c) Hirn's Analysis. — The relation stated in Eq. (130), applied 
in the manner just illustrated, is the working principle of what is called 
Hirn's analysis for the determination of the heat interchanges between 
the steam and the cylinder walls. In brief outline, the scheme is as 
follows : 

The calculation is started at Q, the beginning of compression, 
usually with the assumption that the clearance steam is there dry- 
saturated, which makes its weight a known quantity — see § 25 (i) for 
some special information concerning the state of the steam at this point. 

With steam weight, pressure, and volume known at Q and at J, the 
energies 7q and 7j are easily found. To the initial energy 7q add the 
piston work A Uqj under curve QJ (measured down to the base ON and 
reduced to heat units) ; then if 7j is less than this sum, the difference 
has gone from the steam into the walls, if it is greater the difference 
has come into the steam. 

At no point from J up to A and over to E is it possible to know just 
how much steam is present in the cylinder; but as soon as cut-off has 
made the steam weight definite, the calculation can be resumed. To 
the energy 7j of the clearance steam at J add the total heat Hi which 
the new steam had when it entered the cylinder. From this sum sub- 
tract the energy 7e of the whole steam at E plus the piston work AEFM 
or A Uae ; the difference is the heat given to the walls from J to E. 

In algebraic expression, the heat interchanges just described are, 

0qj=7q+AC/ qj -7j, (131) 

Qje = 7j + Hr - 7 E - AUae; ..... (132) 

and the sum of the two, or the total heat yielded by the steam during 
compression and admission, is 

Qqae =27 1 +7q+^C/qj-7 e -,1*7ae. . . . (133) 

To continue the numerical illustration in the last article, the data 
represented by Fig. 114 may be worked out as follows: 

At Q, with p = 15.7 lb. abs., K = 1077.6, z = 1.00, w = 0.206 lb., 

7 Q = 0.206 X 1077.6 = 222.0 B.t.u. 
The area under QJ is 5.11 sq. in., so that 
AUqj = 22.7 B.t.u. 



§24 (c)] ANALYSIS FOR THERMAL EFFECT. 211 

The entering steam is at 120 lb. abs., for which pressure the total 
heat is 1189.8; with 0.794 lb. of steam coming in, assumed to be dry- 
saturated, 

#i = 0.794 X 1189.8 = 944.7 B.t.u. 

The energy of the steam at E has already been calculated, in Art. 
(6), as 

7e = 941.8 B.t.u. 

By measurement, area AEFM = 11.56 sq. in., or 
AU ae = 51.3 B.t.u. 

Now substitute in Eq. (133) and get, 

Q = 944.7 + 222.0 + 22.7 - 941.8 - 51.3 
= 1189.4 - 993.1 = 196.3 B.t.u. 

At J, p = 70, x = 0.915, 7j = 212.0; then the heat given up during 
compression comes out as 

Q QJ = 222.0 + 22.7 - 212.0 = 32.7 B.t.u., 
leaving 196.3 — 32.7 = 163.6 B.t.u. as the heat surrendered during 
admission. 

An approximation which naturally offers itself is to take the latent 
heat of the steam condensed at cut-off (or of the " missing steam") as 
the heat absorbed by the cylinder walls. Only a very small error is 
introduced by carrying Wi = 0.2 from E up to the initial pressure on 
line PV, Where r\ = 877.6; then m\T\ = 175.6 B.t.u., as against 196.3 
above. Obviously, as compression and throttling during admission are 
less, these two results tend to come into closer agreement; on the other 
hand, if the missing quantity keeps constant while compression in- 
creases — compare § 23 (e) — the heat absorbed by the walls will also 
increase, because the equivalent of the work of compression adds itself 
to the latent heat of the steam condensed. 

Note that in this discussion the symbols 7 and A U are not restricted 
to one pound of steam, but are used in relation to any weight which 
may be present. 

(d) Completion of the Cycle. — The calculation of the heat re- 
turned during expansion, according to the equation 

eES = 7s+A*7 E s-7E, (134) 

has been illustrated in Art. (6). Subtracting the 96.4 B.t.u. there 
found from the 196.3 which the walls have taken up, we have 99.9 B.t.u. 
of this heat yet left in the metal, barring loss by conduction and radia- 
tion. This is, of course, less than the 0.143 X 944.5 = 135.1 B.t.u. of 
I latent heat of the moisture in the steam at S : necessarily, there must 
be some net condensation, because of the performance of the work of 



212 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



expansion. Complete reevaporation is not needed for the assumption 
of dry steam at Q, since a considerable part of the water remaining at 
S will be thrown off the metal surfaces and swept out, in the rapid pres- 
sure drop and outrush of steam from S down to the exhaust pressure. 

To complete the determination and get a "heat balance" for the 
cycle, the condenser must be made to serve as a calorimeter. From 
the weight of cooling water per pound of steam condensed, with its 
initial and final temperatures, the heat content of the exhaust steam is 
calculable, being finally expressed, like all the other quantities, as if 
measured above 32 deg. The energy Is, plus the work A l7 S q done by 
the piston upon the exhaust steam, plus the heat further received from 
the walls, minus the energy Jq, should just equal the heat content 
measured by the condenser. The heat from the walls is the "unknown" 
component, and with absolutely exact experimentation its true value 
would be made known: whereupon, any deficiency from the computed 
residuum could with confidence be charged to radiation. Actually, the 
best accuracy attainable will lead to but a very rough measure (pro- 
portionally) of these relatively small quantities. 



330 
320 
310 
300 




280 

260 

240 
220 



M F 5 V 10 

Fig. 115. — Data for the Temperature-entropy Diagram. 



N 



Granting full accuracy of indicator diagrams and of steam measure- 
ment, but having only these data, there are two points of uncertainty 
in this analysis; one is the real quality of the clearance steam, the other, 
the amount of leakage occurring. The determination of heat rejected, 
by means of the condenser, helps to settle the latter question, except 
as complicated by radiation loss. 

(e) The Temperature-Entropy Diagram. — In preparation for 
its transfer to the temperature-entropy plane, certain preliminary 
work must be done upon the indicator diagram, as is illustrated in 






§ 24 (e)] ANALYSIS FOR THERMAL EFFECT. 213 

Fig. 115. At the right-hand end of that figure, a scale of correspond- 
ing steam temperatures is laid off, and isothermal lines are drawn across 
the diagram at equally-spaced temperatures. Two curves of constant 
steam weight are laid out, CC for one pound of total steam, QRT for 
0.206 lb. of clearance steam — the diagram being the same as in Fig. 
114. For the expansion and compression curves, equilateral hyper- 
bolas are assumed; and this definite form having been chosen, the com- 
pression curve can be extended up to the line of initial pressure at K. 
Two curves of quality x are plotted at the right, GGH for expansion 
and release, LL for compression. A value of x on curve GG is got by 
dividing the abscissa of curve ES by that of curve CC ; similarly, points 
on LL show the ratio of volumes between compression curve QJK and 
const ant- weight curve QRT. For GH, an abscissa of curve SD is 
divided by the value of the steam volume s from Table II ; calling this 
a "quality curve" implies the idea of the steam being condensed within 
the cylinder, roughly at constant volume; which imaginary operation 
is, in effect, substituted for that of actual outflow, when the diagram is 
changed over into the temperature-entropy system of representation. 

The new diagram is laid out in Fig. 116. Having the x curves in 
Fig. 115, it is a simple matter to divide in the ratio x the entropy N r 
or b, included between the curves WU and CC: measurement and slide- 
rule calculation is the preferable method. Diagram WESDU in Fig. 
116 is for the total steam, representing the outline with the same letter- 
ing in Fig. 115. There is no way of transferring the closed indicator 
diagram AESDQR to the temperature-entropy plane without some 
distortion of the entropy abscissas. Even the curves WAE and SDU, 
easily enough laid out from volume ratios, do not by any means repre- 
sent the actual processes of evaporation + inflow + cylinder-condensation 
and of outflow + condensation-of-exhaust : they merely stand for imagi- 
nary thermal actions which would have the same pressure-volume 
effects as are shown by the corresponding curves on the indicator dia- 
gram. Only when the performance of a confined body of steam is in 
question, or when the engine valve is closed during expansion and com- 
pression, can the temperature-entropy diagram be taken to mean 
exactly what it appears to say. 

(/) Thermal Quantities for the Total Steam. — Before going 
on to see how the performance of the clearance steam may be repre- 
sented, we shall consider the determination of heat quantities belong- 
ing to the total steam, as derivable from the profile PAES in Fig. 116. 

If there were no clearance and compression, all of this steam coming 
| in from the boiler and having at entrance the quality corresponding to 
1 the point C, the heat given up to the walls would be the difference 



214 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



between the area under UPC and that under UWAE — these areas 
being bounded by vertical ordinate lines from U, C, and E, and ex- 
tending down to the line of absolute zero of temperature. The effect 
of compression, as set forth in Art. (c), cannot here be shown in any 
simple or effective fashion, so that resort to Hirn's method is necessary 
if the heat transferred to the cylinder walls is to be exactly measured. 



300 




Fig. 116. — Temperature-entropy Diagram from Fig. 115. 

As to the heat restored during expansion, the obvious thing is to 
get the value of the area under ES. By planimeter measurement of 
area ESX, the top of an equivalent rectangle is located at H, at 744 
deg. absolute. The entropy width MN, measuring up as scant 0.129, 
is found by computation from tabular data, with xi = 0.80 and x 2 = 
0.857, to be 0.1293. Then the heat imparted is Q = 0.1293 X 744 = 
96.2 B.t.u., as against 96.4 B.t.u. by the parallel computation in Art. 
(6). The discrepancy is well within the limits of error of the methods 
used. 

Another scheme is based upon an extension of the idea of the Rank- 
ine cycle. Consider the diagram ZEXY in Fig. 116; in the cyclical 
lowering of pressure from ZE to XY, the external work represented 
by the area ZEXY is equal to the difference between total heat hi at 
E and total heat h 2 at X, as is brought out in § 15 (d) and § 16 (b). 
With some other expansion curve than the adiabatic, as ES, and with 
heat Q coming in while the steam is passing from E to S, the heat value 
of the work ZESY will be 

AUzs = h! + Q-h 2 ; 
whence 

Q = AU zs + (h 2 -h 1 ) (135) 

In the particular case of Fig. 115 — that is, with an expansion 
curve of the form pv = C — the difference (h 2 — hi) will be the same 






§24 (/)] ANALYSIS FOR THERMAL EFFECT. 211 

as (1 2 — Ii) in Art. (6) ; also, the area between the curve ES and either 
axis will be the same. Other proportions would better have illustrated 
the general proposition that the area beneath an expansion curve plus 
the change of internal energy is equal to the area from the curve over 
to the vertical pressure axis plus the change of total heat. 

(g) Behavior of the Clearance Steam. — The only way to get 
an exact representation of thermal action during compression, with 
entropy measured on the scale at the bottom of Fig. 116, is to draw 
the curve Q'J' for one pound of clearance steam, using the x curve LL 
in Fig. 115. Then the area under Q'J' is the heat given up by one 
pound of steam in being compressed along the curve pv = C, from 
initial dryness at Q — and similarly with any other actual form of 
curve. 

It is a simple matter to lay out on the main diagram a curve which 
will represent the operations of compression and clearance filling, at 
least so % far as to divide off an area corresponding with the indicator 
diagram: but this will not be a true temperature-entropy line, nor will 
the area beneath it, between vertical ordinates, be equal to heat trans- 
ferred. Having 0.206 lb. of clearance steam in the example under con- 
sideration, draw a constant steam-weight line TQ on Fig. 116, dividing 
all the distances between WU and CC in this ratio. Then locate QJ 
with reference to QT and UW just as Q'J' is located between CC and 
UW. In the diagram, the whole curve QJK is transferred from Fig. 
115, likewise the line JA; the idea under all these constructions being 
to make volume ratios and entropy ratios equal. Of course, the curve 
JA, referred to the line QRT in Fig. 116, has no semblance of physical 
meaning; but the area AESDQJA is equivalent to the indicator dia- 
gram with the same lettering in Fig. 115. 

It is possible to refer to the line QJ, Fig. 116, an area which shall 
represent the heat given up in compression. By the same method of 
proportions as above, transfer the constant-entropy line J'L' to the 
space between UW and QT, where it appears as JL: then the area QJL 
plus the area under QL (the latter between verticals) shows the heat 
which must be abstracted from 0.206 lb. of steam in order that it may 
follow the curve QJ in being compressed through the range of pressure 
indicated on Fig. 115. 

(h) Utility of the Temperature-Entropy Diagram. — Several 
schemes for taking into account the performance of the clearance steam 
in the layout of this diagram have been proposed by different writers, 
but that represented by the outline AESDQJA in Fig. 116 is the one 
commonly used, and seems to be the best. Objections to it are found 
in the lack of correlation between the inner curve JQA and the funda- 



216 



ACTION OF THE STEAM IN THE ENGINE. 



[Chap. V. 



mental meaning of the coordinates of the diagram, and in the fact that 
with multiple-expansion engines the change in weight of clearance 
steam, from cylinder to cylinder, calls for all kinds of unsatisfactory 
expedients. Considering that the expansion curve is the only part of 
the profile with a real physical meaning, the diagram scarcely justifies 
itself as a means of exact thermal analysis and representation : certainly 
the method of Hirn is far clearer and more serviceable for the determi- 
nation of the values of the secondary heat quantities. But if the point 
of view be somewhat shifted and a further slight sacrifice of strict con- 
struction be allowed, the temperature-entropy diagram can be made a 
very simple and useful device for comparing actual with ideal perform- 
ance, or the indicator diagram with the Rankine cycle. The method 
now to be proposed bears some analogy to the elimination of the clear- 
ance steam from the pressure-volume diagram, as in Figs. 75 and 81, 
and the resulting diagram is for the working steam alone. In Figs. 117 
and 118, only the full lines belong to the final scheme; the dotted curves 
merely illustrate certain secondary matters. 



330 




M 5 v 10 

Fig. 117. — Ratio Curves for the Working Steam. 



N 



(i) Ratio Curves for the Working Steam. — In Fig. 117 the 
emphasized quantity is the volume v at any pressure p, as it would 
enter into the work element v dp — see Fig. 67. This v is taken to be 
simply the width across the diagram, or the intercept between curves 
AJQ and AESD, and is therefore what we may call the realized or 
effective volume of the working steam. Continuing our numerical ex- 
ample, the weight of the latter steam is 0.794 lb.; then to get any point 
on the ratio curve A'J'S'Q', the specific volume s from Table II is multi- 
plied by this weight, and the result is divided into the measured v. 
At t = 280 deg., for instance, s = 8.64 and 0.794s = 6.88 cu. ft.; the 
volume v or length CD is 5.49 cu. ft.; then x = 5.49 -s- 6.86 = 0.800 



§ 24 ft)] 



ANALYSIS FOR THERMAL EFFECT. 



217 



is the abscissa of the point on curve J'S'. The name " steam ratio" 
seems more appropriate than " quality fraction" for this x. 

In Fig. 117, the compression curve is produced upward to the line 
of initial pressure, as in Fig. 115; and the expansion curve for this 
weight of steam is also drawn, so as to complete the cycle diagram of 
the clearance steam, after the manner of Fig. 111. In this particular 
case, G is a point on a constant steam-weight curve from Q, like QRT 
in Fig. 115, and represents the full, dry volume of the clearance steam.; 
similarly, V is a point on the one-pound curve for the total steam, there 
CC. The point H is located so as to satisfy the proportion 

FH : FG : : FE : FV. 

The curve LHR is passed through H and made similar to BS. 

The dotted ratio curves are differentiated by the origin of v, at its 



340 




200 

0:5 N 10 

Fig. 118. — Temperature-Entropy Diagram for the Working Steam. 

left-hand end on the diagram, the right-hand end being always on the 
curve AESD. Curve A'J'S'Q' corresponds to AJQ, L'H'S'Q' to KJQ, 
and K'H"S"R' to LHR. With ratios read from these curves and 
applied to the vaporization entropy b, the several curves in Fig. 118 are 
easily plotted. Note that the x curves in Fig. 117 are left incomplete 
at the top: they would all run over to their zero line at MA. 

(j) Thermal Diagram for the Working Steam. — The full out- 
line AEFGD, Fig. 118, represents the indicator diagram AESDQJ, 
Fig. 117, transferred on a strictly volumetric basis to the temperature- 
entropy plane, and there backed up against the water line AD. The 
losses of effect, from all causes, are shown in their combined value by 
the departure from the Rankine cycle ABCD; but there is no exact 
delineation of their manner of occurrence, nor can a detailed analysis 
be made from this diagram. 



218 ACTION OF THE STEAM IN THE ENGINE. [Chap V. 

■ 
■ 

The dotted curves show an approximate analysis of the losses, sepa- 
rating them as regards the agency of their production. Thus if the 
clearance steam was simply an elastic cushion, its volume always ex- 
tending to the curve LHR, Fig. 117, and if there were no kinetic waste 
in filling the clearance space, the working steam would do the work 
represented by the pv area LESDRL or the TN area AJKLDA. To 
the negative clearance-steam cycle directly, but to cylinder-wall action 
ultimately, is due the lost area between AJKL and AHFG, Fig. 118, 
while the kinetic waste in filling the clearance cuts off the area AEHA. 

In favor of this simple but approximate diagram AEFGD, as against 
schemes typified by the outline AESDQJ on Fig. 116, the following 
points may be made: 

The curve QJA, Fig. 116, — although as referred to QT or LK it 
represents fairly well the behavior and effect of the clearance steam, — 
has no direct thermal meaning; and in being located near the left end of 
the diagram, in the region belonging to the early stages of vaporization, 
it entirely contravenes the physical meaning of the entropy abscissas. 

The clearance steam has absolutely no relation to the early part of 
vaporization, but is one of the unfavorable surroundings which, after 
full vaporization in the boiler, the steam encounters within the engine; 
it may be considered as merely an agency through which the cylinder 
walls exert a part of their harmful thermal effect. So far as these in- 
fluences have weight, the proper place to show their effect is at the 
right-hand end of the diagram. 

In a multiple-expansion engine, with different weights of clearance 
steam in the successive cylinders, any method like that of Fig. 116 is 
very troublesome. But diagrams for the unit of 'working steam alone 
can be run right down the series of cylinders, with a common reference 
line in the curve AD. 

For closer analysis, whether of a simple or compound engine, curves 
like ES and Q'J' of Fig. 116 are to be laid out in true form for each 
cylinder, along with the diagram like Fig. 118. 

With either form of diagram, heat received from condensation of 
steam in a jacket can very simply be represented by an area to the right 
of a line like BC in Fig. 118. 

§ 25. Thermal Action of the Cylinder Walls 

(a) Information Available. — The effect of the cylinder walls, as 
expressed and measured by the size of the missing steam quantity, has 
been quite fully considered in § 22 — this resultant generally including 
also a leakage component, which may vary widely in relative magni- 



§ 25 (a)] THERMAL ACTION OF THE CYLINDER WALLS. 



219 



tude. In the last section, methods of calculating and of graphically 
representing the wall effect in thermal measure have been set forth, 
but without the presentation of definite numerical results. Now the 
action of the metal surfaces will be studied more in detail: the con- 
trolling principles can be deduced or inferred, at least in a qualitative 
way, from the small amount of direct experimental data and from the 
relations developed in the last three sections. 

The essential feature of the experimental investigation is the measure- 
ment of the rapidly varying temperature of the metal, and incidentally 
of the steam also. In its requirement of special skill in the use of 
delicate apparatus, this line of investigation far transcends the ordi- 
nary engineering experiment, lying in the domain of the trained physicist. 
The instrument available for strictly localized determination is the 
thermocouple, while the platinum resistance thermometer may equally 
well be used in the steam. The general scheme is to close the electric 
circuit for a short and very definitely located portion of the revolution 
of the crank shaft, say for as little as one-thirtieth, and get the mean 
temperature during this interval. Since the intervals must be meas- 
ured serially, quite a time is required for covering the cycle, during 
which the running conditions must be kept very steady. 

Two prominent sets of experiments fully represent the data now 
available, and comprise the greater part of this body of information. 
They are those of Callendar and Nicholson, made at McGill Univer- 
sity in 1895, Proc. Inst. C. E., 1898, vol. 131, pages 147 to 268; and 
of Duchesne, at the University of Liege from 1904 on, best reported in 
Revue de Mecanique, 1906, vol. 19, pages 1 to 40. 

(b) The Steam-temperature Cycle. — If the steam is and re- 
mains saturated throughout the cycle, its temperature curve can readily 




O M 33 30 21 24 21 N 

Fig. 119. — Typical Indicator Diagrams, prepared for plot of temperature curves. 

be derived from the indicator diagram. In Fig. 119 the three diagrams 
given cover a wide range of power development, showing a steam dis- 
tribution of the constant-compression type, as by the Corliss or the 
double-valve gear. The semicircle on the stroke line MN (which 



220 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V 



merely happens to touch the top line) is divided at every ten degrees 
of crank angle; then ordinates through the division points locate the 
corresponding piston positions, as for an engine with " infinite" con- 
necting rod — see § 31 (b) and (d) for explanation of the relation in- 
volved, and for the modification required when the actual motion of 
the piston is to be more closely followed. As indicated by the scale at 
the right, horizontal lines are drawn at the pressure heights correspond- 
ing to each ten degrees of steam temperature. It is now a very simple 
matter to plot the saturation-temperature curves in Fig. 120, where 
the full-line curve No. 2 has the same lettering as its steam diagram. 































































































A 




■-• 








B 






-^ 










































































v > 






























































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27 



350 
t 

300 
Dec. 

250 
FahR 

200 

Fig. 120. — Curves of Steam Temperature, from Fig. 119, on the 
developed crank circle as base. 

With these curves are drawn the three lines of mean temperature, 
type HK, as averaged on the time base of the diagram. An important 
fact brought out by the experiments is that the mean wall temperature 
is usually higher than this mean steam temperature. 

(c) The Callendar and Nicholson Experiments. — For particu- 
lars of the engine tested, see beneath Fig. 106. In the head and along 
the side of the cylinder, flat-bottomed holes were drilled to within a 
short distance of the inner surface, and the temperature of the surface 
at the bottom of the hole was measured. The thickness of metal left, 
or the depth from within outward, was made as little as 0.01 in., but 
most of the measurements were at 0.04 in. depth. The range of the 
metal cycle was found to be surprisingly low: in the cylinder head it 
was, as an average of seven cycles, 4.3 deg. fahr. at 0.04 in., from which 
was computed a range of 7.1 deg. at the surface exposed to steam. In 
the same seven runs, the average maximum steam temperature (during 
admission) was 327 deg., the minimum about 212 deg., and the mean 
wall temperature 303 deg. On the side of the cylinder the wall tem- 
perature was lower, the mean varying from about 292 deg. near the 
head to 240 at the limit of piston travel (the engine was run single- 
acting), and the range of fluctuation was greater. As noted on Fig. 









§ 25 (c)] THERMAL ACTION OF THE CYLINDER WALLS. 



221 



,x08, the speed of the engine was from 44 to 97 r.p.m., and the tempera- 
ture range varied somewhat with the speed, as is shown in Fig. 124. 

Sample curves are given in Fig. 121, the one marked SS being de- 
rived from the indicator diagram as in Fig. 120. The metal curves 
have the respective ranges 4.9 and 13.5 deg. at the depths named, from 
which are deduced surface ranges of 7.5 and 20 deg. The latter was the 
greatest observed, and its size may have been due to the proximity of 
the narrow, annular space between the inward-projecting head and the 
counterbore, which had a length of 3 in. parallel to the axis of the 



350 

300 
t 

250 

Deg. 
Fahr. 



200 



































5 






















fflM> 
























Mmw, 


















1 


j 




mm 


'6i444fW, 




- 








, 


1 


2 




y- 


__- 


„-— 


""V~ 


--■.._ 
















































\ 












3 












\ 










3 
















\ 
























\ S 












fa 












V 
























\ 








S 



























270 



O Deg.Circ. 90 



180 



270 



Fig. 121. — Callendar and Nicholson Curves: SS, steam temperature; 1 — 1, cylinder 
head at 0.039 in. depth; 2 — 2, side wall just inside of face of head, at 0.037 in 
depth; 3 — 3 mean steam temperature. Speed 44 r.p.m.; test No. 1 in Fig. 106. 

cylinder. Perhaps the cleaner condition of the rubbing surfaces will 
account for the fact that greater ranges were generally observed there 
than in the cylinder head. 

(d) Calculation of Heat Absorbed. — By methods of mathe- 
matical physics, of which only the barest outline is appropriate here, 
the amount of heat alternately absorbed and given off by the metal 
wall may be approximately computed when the range of temperature 
at a known depth has been measured. If the temperature in the in- 
definitely thin surface layer varies periodically in a definite manner, 
there will be a similar cycle in the deeper layers: the amplitude of 
the variation decreases with the depth, and the period lags more and 
more behind that at the surface. The only form of cycle calculable 
with any degree of ease is the simple harmonic, in which the tempera- 
ture t follows a sine curve in terms of time, the complete period 2 it 
being equal to the time of one revolution of the engine. Compare the 
inertia-force curves of this form in Fig. 192, also " harmonic motion" in 
§31 (6). With this cycle the temperature range at increasing depths 
lies between limit curves such as AC and BC in Fig. 122. These are of 



222 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



the form t = e~ mx , where x is the depth from surface AB, according to 
the scale at the bottom, and m is a function of the specific heat and 
conductivity of the metal and of the revolution period 1/n seconds. 
Since depth measures volume, hence heat capacity, the area between 
the curves, as ACB, is proportional to heat absorbed. Since, however, 
the temperature along the limit curves like AC and BC is not reached 
simultaneously, but in sequence by the successive layers, the whole 
heat measured by the area ACB does not go in and out, a portion of it 
simply flowing back and forth within the metal. The factor for the 
heat which really passes the surface AB is 0.707 or Vj. 



+ 5 



Deg. 
Fahr. 



-5 



\ A 












\ 












\ 












\ 












\ 

s 


V 








,9 


1 ■ 
























\ 










£ 


\ 










Ot 


b 










D.T 



\8 


















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^ 


4 








• 








.___-- 


~rrrr_~ 


3 






~~G"" 
















E 



500 
400 

300 

F 

200 

100 
B.T.U 



0.2 IN. 



N 100 R.p.m. 200 



300 



400 



Fig. 122. — Limit Curves 
of temperature range: 
ACB for 25 r.p.m., 
ADB for 250 r.p.m. 
Simple harmonic cycle. 



Fig. 123. — Curves of Heat Absorbed, per square 
foot of surface and with a surface range of 10 
deg. fahr.; EE, heat per cycle, FF heat per min- 
ute. Curve GG, temperature range at 0.04 in. 
depth. 



Directly applicable results of the calculation are given in Fig. 123: 
curve EE shows an absorption per cycle per square foot which varies 
from 4 down to 1 B.t.u. with a change from 25 to 400 r.p.m., while FF 
shows a total transfer, in each of the two directions, amounting to from 
100 to 400 B.t.u. per square foot per minute. These are for a surface 
range of 10 deg. , and will vary in direct ratio to_ any other range. The 
ordinate of EE is inversely proportional to ViV; and when it is multi- 
plied by N to give the heat per minute, this makes the latter quantity 
vary directly as ViV. Curve GG shows the calculated range at 0.04 
in. depth, with a surface range of 10 deg. as related to speed N. 

(e) Influence of Speed. — It is of interest to see, in a general 
way, how the showing of Fig. 123 (for a constant surface range) will be 
modified by the variation of actual range with speed. For the experi- 
ments under consideration, the latter relation is set forth in Fig. 124. 
Approximately, the range is inversely proportional to some low power 
of N, or to N a when a is a small fraction. Then the actual heat ab- 



§25 (e)] THERMAL ACTION OF THE CYLINDER WALLS. 



223 



sorbed per square foot per cycle, which corresponds directly with the 
steam condensed per cycle, will vary inversely as N°- 5+a , the heat per 
minute directly as N°- 5 ~ a . The missing steam on account of leakage is 




Fig. 124. — Variation of Temperature Range with Speed, in the metal of the cylinder 
head. Curve AA, observed range t at 0.04 in. depth; BB, calculated range at 
the surface; odd point marked on ordinate 4 shows one determination at 0.013 
in. depth. 

also some inverse function of N, sq that the general tendency is to 

make the total missing quantity vary as N - Qmb+a+b , while the amount per 

minute will be proportional to N°*~ a ~ b . In other words, the actual 
quantities vary more rapidly than the ordinate of curve EE, less rapidly 
than that of FF. 

At first sight there seems to_be a serious disagreement between this 
conclusion and the divisor ^N, as found empirically for use in Eq. 
(126) ; but the less rapid variation of the missing fraction m with speed 
— because N has a smaller exponent in the formula — is compensated 
by a change in the total steam received per revolution; which increases 
as the speed falls off, other conditions remaining the same, because of 
greater initial condensation. An attempt to bring the matter of the 
last paragraph to definite, quantitative expression, with the data be- 
fore us, would be futile and fruitless; but a comparison of Fig. 100 with 
Fig. 123 shows a close similarity in the manner of variation of the steam 
condensed and of the heat absorbed per cycle. 

(/) Calculation from the Steam-temperature Curve. — As 
appears from Fig. 121, the actual temperature cycle in the metal is 
not of the simple harmonic form. For an extreme case of concentra- 
tion of the rapid fluctuation into a short portion of the total period, the 
authors of the paper give the result of calculations upon an assumed 
cycle ; they state that while the surface range, as deduced from measure- 
ments at say 0.04 in. will not agree with the relation represented in 
Fig. 123, the heat absorbed will be nearly the same. Using then the 
quantities computed for the harmonic cycle, they establish the follow- 
ing simple method: 

In Fig. 121, the shaded area at the top of the diagram SS shows by 
how much and for how long the temperature of the steam is above that 



224 ACTION OF THE STEAM IN THE ENGINE. [Chap V. 

of the metal. Only during this period will heat pass from the steam 
into the metal; and the rate of transfer is taken to be proportional to 
the difference of temperature — which ^s only an approximate assump- 
tion. Then the product of temperature difference in degrees by time 
in seconds, or the shaded " condensation area" expressed in degree- 
seconds, will be a measure of the amount of heat given up by the steam 
to the metal. With the small ranges observed in these experiments, 
the line of mean wall temperature may very effectively be used as the 
lower boundary of the condensation area. 

By comparing values of this area with the amount of heat absorbed 
by the metal according to curve EE of Fig. 123, a fairly constant ratio 
was found to exist; the mean value obtained for the factor by which 
to multiply area in order to get B.t.u. was 0.60 for the more regular 
cycles in the cylinder head, with a range from 0.53 to 0.67. An example 
will best show the method of calculation. 

As originally drawn, Fig. 121 had the scales 1 in. of base = 40 deg. 
of angle, 1 in. of ordinate = 32 deg. of temperature. The speed being 
43.8 r.p.m., the time of one revolution is 60 -r- 43.8 = 1.37 seconds, of 
which one-ninth (or 40°) is 0.152 sec. Then one square inch of diagram 
area equals 32 X 0.152 = 4.86 degree-seconds. The measured area 
above curve 1-1 in Fig. 121 was 0.88 sq. in., equivalent to 4.28 deg. sec; 
and multiplying this by 0.6 we get the heat absorption 2.57 B.t.u 
Taking from curve EE, Fig. 123, the rate 3.00 at 43.8 r.p.m., and using 
the factor 0.75 because the range at the surface is 7.5 instead of 10 
deg., we have 2.25 B.t.u. as the heat absorbed by the metal per square 
foot per cycle. The agreement between 2.57 and 2.25 is not very good, 
but this happens to be one of the extreme cases, that in which the 
factor for condensation area worked out 0.53 instead of 0.60. 

This scheme is attractively simple, especially if the easily-measured 
mean wall temperature may be used as the lower limit of the condensa- 
tion area. It fails, however, to check up well, even over the com- 
paratively small range of these experiments. Thus, if the growth of 
heat absorption with decrease of speed is to be accounted for, the 
difference between maximum steam temperature and mean wall tem- 
perature ought to become greater with lower speed; actually, for the 
seven tests plotted in Fig. 124, the difference is practically constant at 
24.5 deg., with an irregular variation from 23 to 26 deg. 

(g) Rates of Heat Absorption. — In these experiments, the rate 
of heat absorption per square foot per minute ranged from 100 to 130 
B.t.u. for the surfaces which were, on the average, about 25 deg. below 
the steam temperature during admission (this 25 deg. being the height 
of the shaded " condensation area" in Fig. 121); other parts of the 



§ 25 (g)] THERMAL ACTION OF THE CYLINDER WALLS. 225> 

interior surfaces had higher rates. This is equivalent to a transfer of 
4 to 5 B.t.u. per minute per degree of difference between steam and 
metal; but if we allow for the fact that the absorption took place dur- 
ing about one-fifth of the revolution, the corresponding steady rate 
would be from 20 to 25 B.t.u. per square foot per minute per degree of 
difference. 

The latter measure of the rate is deduced because of a desire to 
compare it with the performance of the tubes in a surface condenser. 
A very complete collection of the information existing on the subject 
of heat transfer in the condenser will be found in a paper by Mr. G. A. 
Orrok in Journal A. S. M. E. for Nov., 1910, vol. 32 of the Transac- 
tions. In his Fig. 9 are shown rates ranging from 400 to 1000 B.t.u. 
per hour per square foot per degree of difference between the steam 
on one side and the water on the other side of a thin wall of brass, the 
rapidity of the water circulation being the controlling variable: the 
corresponding rate per minute is 7 to 16 B.t.u. To attempt a close 
comparison of the physical conditions in the two cases is not worth 
while, but it is of interest to note that the rather low rates of cylinder- 
wall absorption deduced above are considerably greater than those 
maintainable in the condenser. 

(h) Rates of Condensation. — The Callendar and Nicholson ex- 
periments and methods of calculation have been quite fully described, 
because they represent an almost unique attempt to measure the heat 
absorption on the side of the metal, instead of deducing it from the 
missing steam quantity. That the actual quantitative results are 
typical seems rather unlikely, because the heat rates which they show 
would generally come far short of accounting for the apparent con- 
densation, and it is difficult to accept the hypothesis of always preva- 
lent leakage sufficient in amount and regular enough in action to bridge 
the gap. 

In that engine, the amount of heat alternately absorbed and given 
off by the cylinder walls varied from 6000 to 12,000 B.t.u. per square 
foot per hour (for the different surfaces), equivalent to a condensation 
of 7 to 14 lb. of steam at about 90 lb. gage pressure: and the clearance 
surface was 3.74 sq. ft. Apparently calculated by the condensation- 
area method, the condensation per hour is given as 39 lb., which is 
not made to vary with the speed — to be explicit, this accounts for 
line 17 in Table VI of the paper. The missing steam, represented by 
the length BD on Fig. 106 and got from MB as determined by taking 
the difference between the very large leakage AB and the total steam 
used, ranged from 31 to 57 lb. per hour (with no clear relativity to 
speed), and gave an average of 43 lb. Referred to the 3.74 sq. ft. of 



226 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



clearance surface, the measured missing quantity was from 0.0020 to 
0.0042 lb. per square foot per cycle. 

A few data from the tests diagrammed in § 22 will give an idea of 
the comparative magnitude of these rates. The 17 by 30 in. non- 
condensing engine of Figs. 86 and 87 had a clearance surface of 5.81 
sq. ft., and the missing steam per square foot of this surface per cycle 
was from 0.013 to 0.046 lb., the high value belonging to very low speed: 
at similar speeds this is equivalent to about four times the Callendar 
and Nicholson result. In the Willans engine, Fig. 96, the missing 
quantity on the same basis was from 0.0004 to 0.0038 lb. (this range 
covering the three different sizes of cylinder), but the speed of 400 
r.p.m. must be taken into account when making comparison. 



400 



350 

t 

300 

Dec 
Fahr. 

250 



200 































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K \ c 




















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1 


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So 








1 

1 ," 










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— " 








^yj 


D / 


ipf 








v \V 












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h 'C 










\- — 


*- — --_ 


_ W D 




— 


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7/ 






















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270 



Dec . 90 Circ. 



180 



270 



Fig. 125. — Temperature Curves, from observations by Duchesne (subscript D) 
and by Callendar and Nicholson (subscript C). Curves P, steam temperature 
from pressure, as in Fig. 120; curves S, steam temperature by thermometer; 
curve W, temperature of wall surface. 



(i) The Duchesne Experiments, already referred to in Art. (a), 
have been made upon the 300 by 600 mm. experimental engine in the 
laboratory of the University of Liege, of which the performance under 
certain conditions has been diagrammed in Figs. 109 to 111. The tem- 
perature of the steam was measured by means of a multiple-junction 
thermocouple, in most of the tests at a distance of 15 mm. (0.6 in.) 
from the cylinder wall, in some at 1 mm. distance. For the wall, the 
couple was in the form of a leaf or thin strip of sheet metal, the soldered 
junction of the silver and platinum halves touching the cast-iron sur- 
face, but not adhering in any way. Results from a noncondensing 
run are given in Fig. 125, replotted from the original diagram, and 



§ 25 (i)] THERMAL ACTION OF THE CYLINDER WALLS. 



227 



with them a couple of analogous curves obtained by Callendar and 
Nicholson. 

To describe the latter first, the curve Sc shows results got by measur- 
ing the steam temperature in a little pocket formed by drilling a f-in. 
hole into the thickness of the cylinder head. Strongly affected by the 
metal in such close proximity, the steam is superheated almost through- 
out the cycle, and shows a considerable degree of adiabatic rise during 
compression. But when these experimenters mounted their platinum 
thermometer upon the piston, in such a fashion as to bring it out into 
the body of the steam, there was continual practical agreement be- 
tween pressure temperature and measured temperature. The ther- 
mometer was held in the line of the piston axis, with the exposed wire 

350 



300 

t 

250 
Deg. 

200 

Fahr. 

150 



270 Deg. 90 180 270 

Fig. 126. — Temperature Curves by Duchesne, engine condensing, cut-off at 0.1 
of stroke, compression through 0.6 of stroke. For scheme of diagram, see 
Fig. 125. 

at 3 in. distance from the face of the piston. To give room for the 
projecting thermometer, a capped nipple of 1 in. pipe was screwed into 
a hole drilled at the middle of the cylinder head. As a consequence of 
this arrangement, the active part of the thermometer was, during 
nearly the whole of the compression period, within a narrow space and 
apparently subjected to a strong wall influence. Unless accounted for, 
possibly, by the presence of water, the fact that the steam remained 
saturated is a distinct failure to confirm the Duchesne results. 

Turning now to the Liege experiments, the most striking thing 
seen in Fig. 125 is the superheating of the clearance steam, which begins 
to appear before the end of exhaust and is very marked during com- 
pression. This shows that the latter operation is in large degree adia- 









— \ — 
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1 




W 




















; 




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-\ 
























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228 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



batic, the walls having become dry before the pressure rise begins, and 
the rate of heat transfer therefore being low. When condensation is 
once started, it proceeds very rapidly, and the steam temperature falls 
to that of saturation. The same kind of action, even more pronounced 
in magnitude, is shown in Fig. 126, where the S curve which runs off 
the plane of the drawing has an apex at 525 deg. fahr. 

The apparent range of temperature of the wall surface is about 
40 deg. in Fig. 125, about 130 deg. in Fig. 126. Whether the thermo- 
couple has always the same temperature as the skin layer of the cast- 
iron wall which it touches, is certainly a debatable question. There is 
good reason to believe that the steam will have some influence, the thin 
leaf of metal taking a temperature somewhere between those of cast 









s S 


v 






















/ 




\ 


















350 


3 




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i 


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t 


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/ 




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250 




I 


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Is 


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CH^ 


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v 


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200 


/ 


( 










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/ 


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/ 


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j 


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1 

1 














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^^ 




150 




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r 


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Fig. 127. 



270 DEG. 90 180 270 

Temperature Curves under Various Conditions as to Steam Jacketing. 



iron and of steam, although probably much nearer the former. That 
there may be a considerable variation in the effectiveness of contact is 
suggested by the fact that the two ranges quoted above have between 
them a difference much greater than any possible difference between 
the amounts of heat transferred, or of steam condensed and reevapo- 
rated, in the respective cases. Making every allowance for these 
uncertainties, there is indubitable indication of a real surface range 
decidedly greater than was found in the Callendar and Nicholson 
tests. 

Yet another set of these results is given in Fig. 127, of interest here 
and also in connection with the subject of steam jacketing. The three 
types of curves are distinguished by the kind of line, as in the preced- 



§ 25 (i)] THERMAL ACTION OF THE CYLINDER WALLS. 229 

ing figures. The respective conditions are: case 1, no steam in jackets; 
case 2, jackets filled with steam of boiler pressure; case 3, jacket steam 
of higher pressure and temperature (amount not stated). Note the 
successive elevation of the mean wall temperature, and the accompany- 
ing diminution in its range of fluctuation; also how the superheating of 
the steam during exhaust and compression increases as the wall is hotter. 

(j) Conclusions. — It is very evident that the data presented are 
neither sufficient in amount nor in good enough agreement to be formu- 
lable into even an empirical theory of wall action; they do serve, how- 
ever, to elucidate some important principles. 

That the mean temperature of the cylinder walls is generally a good 
way above the mean of the steam temperature indicates that the free- 
dom of heat transfer from steam to metal is greater than from metal 
to steam. This is highly reasonable under the conditions of the steam- 
engine cycle, for when giving up heat the steam is at high pressure, 
when it is receiving heat the pressure is low and falling. Probably, 
conductivity increases slowly with density; but the stronger influence 
is the rising or steady high pressure, which holds the moisture of con- 
densation against the metal; and while water is a poorer conductor 
than iron, the wetness of the surface promotes the yielding of heat by 
the vapor. As the pressure falls, the film of water will tend to be 
thrown off by the formation of steam beneath it; and with a sudden 
drop of pressure at release, a good part of the water mixed with the 
steam is likely to be swept out unevaporated. By these mechanical 
actions, as well as the simple outflow of heat, the layer of steam close 
to the metal is made dry, and thus the freedom of heat transfer is yet 
further diminished. 

Callendar and Nicholson advance the proposition that as the in- 
fluences favoring cylinder condensation grow stronger, the mean wall' 
temperature will fall; but that the lower limit is the mean temperature 
of the steam, as fixed by its pressure. When this limit is reached, 
water may accumulate in the cylinder; or, at least, moisture will be 
present throughout the cycle, even though any great accumulation is 
prevented by the mechanical action of the steam currents. These 
hypotheses suggest a rational idea of the influence of moisture in the 
entering steam: if the condensation is less than the limit just described, 
so that the cylinder walls are dry at the beginning of admission, the 
degree of wetness of the new steam may exert a considerable influence; 
but if the cylinder action is strong, and the walls already moist when 
admission begins, a little more water in the entering steam makes very 
little difference. This is in accord with experience. 

The " condensation-area " method of Callendar and Nicholson can- 



230 



ACTION OF THE STEAM IN THE ENGINE. [Chap. V. 



not be considered as satisfactorily established. The general idea may 
be correct, although subject to secondary influences not yet clearly 
seen; but the reduction factor deduced from their tests is not to be ac- 
cepted without confirmation by other and far more extensive measure- 
ments of temperature range in the metal. There is certainly no 
sufficient reason for substituting a scheme of calculation or estimate 
based upon temperature observations for the more direct determina- 
tion of (probable) missing quantity by the method of Eq. (126). 

A very great practical disadvantage of the whole plan of direct tem- 
perature measurement, as a means of investigation, is found in the non- 
uniformity of condition within the cylinder; whence observations so 
strictly localized must be made at a number of different points, in order 
that the prevailing mean may be ascertained. Against this, the indica- 
tor diagram gives a net result, perhaps of very heterogeneous con- 
ditions, but all the more useful because it is their net effect. 



CHAPTER VI 
PERFORMANCE AND EFFICIENCY OF THE ENGINE 

§ 26. Measures of Performance 

, (a) Steam Consumption. — The most obvious and the most gen- 
erally used measure of the thermodynamic performance of an engine 
(or of a turbine) is the steam consumption per unit of work output. 
For the piston engine, the latter unit is commonly the horse-power- 
hour; and because the indicator offers the easiest means of measuring 
engine output, the indicated power, at the piston, is much oftener used 
than the effective or " brake" power. In the service of driving electric 
generators, the electrical output in kilowatts is both more important 
and more readily known than the steam horse-power; with the turbine, 
in fact, the latter can be found only by inference, through an esti- 
mate of machine losses. For these reasons, steam per kilowatt-hour is 
a much used measure of performance. The relative values of the 
several output units are as follows: 

1 horse-power-hour = 1,980,000 ft. lb. = 2545 B.t.u. 

= 0.746 kilowatt-hour. 

1 metric horse-power-hour = 270,000 mkg. = 0.9863 English h.p.h. 

= 0.736 kw.h. 

1 kilowatt-hour = 1.3405 Eng. h.p.h. = 3412 B.t.u. 

For the steam rate, the symbol S will be used. When distinction is 
necessary, Sh will be pounds per horse-power-hour, Sk pounds per kilo- 
watt-hour. The relations are, 

1 lb. per h.p.h. = 1.340 lb. per kw.h. 

= 0.4474 kg. per met. h.p.h. 
1 lb. per kw.h. = 0.746 lb. per Eng. h.p.h. 

= 0.4536 kg. per kw.h. 
1 kg. per met. h.p.h. = 2.235 per Eng. h.p.h. 
= 1.359 kg. per kw.h. 
(b) Actual Steam Rates. — The consumption per indicated horse- 
power-hour, or *Sh, varies from more than 100 lb. in small steam pumps 
down to just about 9 lb. in the best engines and turbines with highly 

231 



232 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

superheated steam. For several important classes of engines, good 
average performance, with saturated steam, is about as follows: 

Small noncondensing engines 30 lb. 

Large noncondensing engines 25 " 

Locomotives 24 " 

The medium range of condensing engines '. . 17 " 

Big and well kept power engines 13 " 

The best pumping engines 11 " 

Only among engines of the same general class, especially as to 
pressure limits and as to kind of steam used, is the consumption S a 
good standard of comparison. For the plant as a whole, and with 
emphasis upon the idea of efficiency, this measure may be quite mis- 
leading, because of wide variation in the amount of heat required, from 
the fire, to make one pound of steam. Thus the locomotive, almost 
never supplied with a feed- water heater, must use cold feed water; 
and in winter its pound of high-pressure steam may require 180 B.t.u. 
more than the same weight in a stationary noncondensing plant with 
a good exhaust-steam heater. Again, S = 9 in a high-superheat engine 
is little, if any, better than S = 11 with saturated steam. And as an 
extreme case, engines with the regenerative cycle of Fig. 59 use more 
pounds of the same kind of steam than do those with the common 
cycle, for the same or better efficiency. Refer to Table 13, page 268, 
and compare tests Nos. 39 and 40 with the just preceding results from 
ordinary pumping engines. 

(c) Thermodynamic Efficiency. — The work done per pound of 
steam, preferably expressed in heat units, so that the symbol would be 
A U in the terms of Chapter IV, and now represented by W, is 

W = ?^ = ?il?B.t.u (136) 

Oh ok 

as already used in § 22 (e). With £ h ranging from 30 lb. down to 10 lb., 
W will lie between 80 and 250 B.t.u. Preparing now for an extensive 
application of the ideas set forth in § 8 (g), we see that W is useful for 
comparison with the heat Q required from the fire to make one pound 
of steam, in order to get the absolute thermal efficiency 

W 
#a = ^; (137) 

also, that by comparing it with the output Wr of the unit of steam in 
the ideal (Rankine) cycle, computed as in § 15 (d), is obtained the 
relative efficiency 

E * = h (138) 



§ 26 (c)] MEASURES OF PERFORMANCE. 233 

In The Steam Engine, Vol. II, Chapter XIII, are given tables 
showing results from tests of more than 110 engines, in all of which the 
efficiencies just defined are worked out. Some of the more prominent 
of these tests are discussed in the next section, and set forth in Table 
13. A general idea of realized results, as to absolute efficiency, can be 
got from the following summary: 

Type of Engine. Efficiency. 

Simple engines 0.07 to 0.13 

Locomotives 0.09 to 0.13 

Medium and large power-service engines, in- 
cluding cases with moderate superheat. 0.12 to 0.18 

The best power engines 0.18 to 0.20 

Modern high-superheat compounds 0.19 to 0.21 

High-grade pumping engines 0.18 to 0.22 

Good average marine engines 0.15 to 0.17 

The relative efficiency ranges mostly from 0.60 to 0.67, sometimes 
rising above 0.70 and seldom falling below 0.50 except when the con- 
ditions of working are very bad, or the engine is much underloaded or 
overloaded. The upper limit is about 0.75 in condensing engines and 
0.80 in noncondensing — see the column for En in Table 13. These' 
limits are approached by only the best engines, large and in good con- 
dition. . The application of relative efficiency as a criterion of per- 
formance is more fully discussed in Art. (k). 

(d) Heat in the Feed Water. — In determining the amount of 
heat to be charged as input Q, several questions arise. If the purpose 
is to find the efficiency of the whole plant, the obvious and proper thing 
is to use both feed temperature and steam quality as measured near 
the boiler: applying these as in § 13 (d), we get the heat actually re- 
ceived from the fire. But if the engine is to be judged by itself, and if 
comparisons are to be made among engines, losses due to the other 
elements of the plant must be eliminated. In the ideal cycle, § 15 (d), 
the temperature of the feed water is that of the steam exhausting from 
the engine. The open feed- water heater, in which the water falls in 
spray through an atmosphere of exhaust steam, will deliver water 
within five degrees of the exhaust temperature, if not worked too 
rapidly: but so far as the exhaust from the main engine is concerned, 
this device is available only in a noncondensing plant. The surface 
heater will generally show a larger gap, say from ten degrees upward, 
according to the rate of water flow relative to the amount of heating 
surface. Allowing for some loss from the feed pipe, often not well 
covered, the heat qo in the feed water is likely to be from 5 to 15 B.t.u. 



234 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

less than the value corresponding to the exhaust temperature. From 
this best operation of the heating system, conditions range down- 
ward, through all degrees of low effectiveness, to the feeding of cold 
water. 

It would be most logical to establish or assume an average deficiency 
in the heat q , saying that with a good feed-water system this would be 
so many heat units less than at exhaust temperature, and thus including 
the unavoidable loss in the working of the engine. Uncertainty as to 
the proper allowance makes the following scheme more desirable: 

To get the engine efficiency alone, use an ideal temperature t for 
the feed water; this will be either the actual temperature of the steam 
in the exhaust pipe, or with jackets, as described below, some higher 
temperature. 

For boiler efficiency, use the temperature in the feed pipe taken near 
the boiler, beyond the feed heater and pump. When the boiler is fed 
by an injector, the low temperature in the suction pipe of the latter 
will generally be taken as the feed temperature — see the elaboration of 
this matter in Art. (h). An economizer is to be considered as a part 
of the boiler, since the heat which it saves is a part of the heat of 
combustion. 

(e) Ideal Feed Temperature. — When the engine is provided 
with steam jackets or reheater coils, in which water collects by con- 
densation but need not fall below the temperature of the steam from 
which it is condensed, the ideal action would be the return of this water 
to the boiler without the loss of any of its heat. If it can be mixed 
with the main current of feed water, coming from the perfect heater at 
exhaust temperature, the result will be the limiting feed temperature 
for the particular engine. Suppose, for instance, that in an engine 
which receives steam at 120 lb. abs. the amount condensed in the jackets 
is 10 per cent of the total, all the jackets carrying full pressure, and 
that the exhaust temperature is 110 deg. At p = 120, t = 341 and 
q = 312; at 110 deg. q is 78. Then 0.1 lb. of hot water from the jackets 
will contain 0.1 X (312 - 78) = 23.4 B.t.u. above 110 deg., and will 
raise the temperature of the whole pound (including itself) to 133.4 
deg., which is therefore the ideal temperature in this case. 

(/) Various Efficiencies. — When Eq. (137) is to be applied to 
the plant as a whole, all the heat Qh absorbed from the fire by the 
boiler, per unit of engine output, must be charged against that out- 
put. For the engine alone, only the heat Q e carried by the steam 
which goes into the engine should be charged. The difference between 
Qb and Q e represents heat which is used up in driving the auxiliaries, 
dissipated in steam-pipe losses, or required to make up deficiencies in 






§ 26 (/)] MEASURES OF PERFORMANCE. 235 

the feed-heating system: its apportionment among these objects may 
be a matter of considerable complexity. 

The efficiency of the engine, when calculated with the ideal feed 
temperature and with steam of the quantity and quality delivered by the 
separator, is the limit of attainable plant efficiency, more nearly ap- 
proached as the pipe losses are less, the feed heater more effective, and 
the auxiliaries more economically operated. Before illustrating the cal- 
culation of efficiencies and the distribution of losses, it will be necessary 
to consider more fully the behavior and the influence of the minor 
members of the plant. 

(g) Working of the Auxiliaries. — These consist of the feed 
pump, the condenser pump or pumps, and sometimes special pumps 
for returning jacket water, circulating oil, etc. With very uniform 
loading, as in a pumping-engine plant, they may be coupled to the 
main engine, and then consume a small portion of its output of power; 
in some modern steam-electric plants, the auxiliaries are driven by 
motors, again drawing upon the main output; but by far the common- 
est scheme is to use separate steam-driven pumps. In developing 
from 2 to 5 per cent of the power of the engine, in a condensing plant, 
the pumps are likely to use from 5 to 20 per cent of the total steam 
consumed — the larger ratio belonging to smaller plants and accom- 
panying poorer conditions in design and maintenance. 

A minimum in the thermodynamic cost of operating the auxiliaries 
is attained when their exhaust, all of it if possible, is used to heat the 
feed water. Whether by drawing from the hot well or by having a 
tubular heater in the exhaust line of the engine, a good approach to 
the temperature of the exhaust steam can be made. Between the tem- 
perature thus fixed by the main engine and the maximum of 212 deg. 
for water under atmospheric pressure there is room for the absorption 
of a considerable amount of heat, perhaps 100 B.t.u. If the exhaust 
from the pumps does not carry more than this much available heat 
per pound of feed water, it can all be condensed by the latter and 
either taken into the main current (if properly freed from cylinder oil), 
or at least thrown away as water but little hotter than the final feed. 
If this return or " regeneration" of the heat supplied to the auxiliaries 
is complete, the operation of the latter costs almost nothing, or merely 
the insignificant heat equivalent of their useful work. 

(h) Feed-water Data. — How to fix upon the proper weight and 
temperature of the feed water, in the scheme of working just outlined, 
can be made clearer by considering the closely analogous case of feed- 
ing the boiler by an injector — the action of the latter being described in 
§ 52. Per horse-power-hour of the engine, the injector draws Wi lb. of 



236 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

water at t x deg.; and by the admixture of live steam increases the 
weight to w 2 and raises the temperature to t 2 . Barring radiation loss 
and the little bit of work done in pushing the water into the boiler, 
all the heat of the steam supplied to the injector is returned as heat. 
The effect is that of a live-steam feed-water heater. So far as the amount 
of heat delivered to the engine, from the fire, is concerned, it is imma- 
terial whether we take Wi lb. of steam from water at h or w 2 lb. from 
water at t 2 . The latter represents more truly the manner in which the 
heat is received from the fire; but the former is decidedly the proper 
form of quantity to be used with the engine. The net feed (wi lb.) 
enters into the main cycle of the plant; the increase (w 2 — Wi) runs 
parallel with wi for a little way, then turns off into the secondary cycle, 
between boiler and injector, in which it keeps up a continual circulation. 
The application of the ideas set forth in this and the preceding 
articles can best be shown by means of an example. To formulate 
rules covering all the cases which are likely to be met with in steam 
plants would be a laborious and space-filling task. Sometimes, con- 
ditions are very simple; very often a number of secondary quantities 
are involved, more or less difficult to measure, some of them perhaps 
derivable by inference. A clear understanding of principles, with 
some ingenuity, is the proper equipment for such work. 

Example 31. — In a pumping-engine -plant, cold water at 52 deg. is drawn 
through a surface heater located between engine and condenser, and raised to 
102 deg. by heat from the main exhaust; it then passes to an open heater, where 
the exhaust from the auxiliaries and the hot water drained from the jackets and 
separator combine with it to form a mixture of 205 deg. temperature. At the 
boiler the steam has a pressure of 162 lb. abs., and contains 0.6 per cent of 
moisture; at the engine, beyond the separator in the steam pipe, the pressure 
is 158 lb. abs. and the quality 0.995. 

In a test of this plant, the jacket and separator drains were cut off from the 
heater; the several discharges were passed through calibrated measuring ves- 
sels, and then allowed to run to waste. The open heater now produced a tem- 
perature of 168 deg., and the feed water was weighed between this heater and 
the pump. The following quantities were determined: 



IC (C 

11 (( 



Weighed feed water 5240 lb. per hour. 

Drained from the engine separator 66 " 

Measured jacket water 746 " 

Drained from oil and water separator of 

open heater 124 " " 

Indicated power of engine 448 i.h.p. 

Analyze this test for steam rates, efficiencies, etc. 

A. Determine the steam consume'd by the auxiliaries. 



§ 26 (h)] MEASURES OF PERFORMANCE/ 237 

Since the exhaust from the pumps passes through a separator before it 
enters the open heater, we assume it to be made nearly dry at atmospheric 
pressure, taking 1140 B.t.u. as its total heat. The hourly weight x lb. of this 
steam may be thought of as condensed and cooled to 102 deg.; then the 1070 a; 
heat units which it thus gives off suffice to raise the whole 5240 lb. of feed 
(including the condensed steam) from 102 to 168 deg. By the equation 

1070 z= 5240 X66, 

we find x to be 323 lb. Adding the oil-separator drainage, the total consump- 
tion by the pumps is 447 lb. 

B. Check the jacket and steam-separator discharge, of 812 lb. weight. 

It is reasonable to assume that the consumption of steam by the engine, 
in whole and in parts, will not be modified by the change in arrangements 
found necessary for weighing the feed water. Then only 5240 — 812 = 4428 
would normally come from the supply and the pump exhaust; and the heat 
given up by the latter, still 1070 X 323 = 345,600 B.t.u., would raise this 

weight by 

345,600 ■*■ 4428 = 78.0 deg., 
or from 102 to 180 deg. 

The raising of the whole 5240 lb. of water from 180 to 205 deg. requires 
5240 X 25 = 131,000 B.t.u.; so that above 180 deg. each pound of hot water 
returned must give off, in the ordinary working of the plant, 

131,000 4- 812 = 161 B.t.u. 

At the steam pressure of 158 lb. abs., the temperature is 363 deg. and the heat 
of the liquid 334.5 B.t.u.: between 334.5 and (180 — 32) there is a difference of 
186.5 B.t.u. which might be carried, as available heat, by the pound of water 
from the high-pressure system. Comparing this with the 161 B.t.u. actually 
delivered, we see the effect of a reasonable loss by radiation plus that of the 
use of steam of reduced pressure (and temperature) in some of the jackets. 

C. The steam (or water) quantities per hour now work out as follows: 

Total water pumped into boiler 5240 lb. 

Used by auxiliaries 447 " 

Sent to main engine 4793 " 

Drained from separator 66 " 

Used by main engine 4727 " 

Used in jackets 746 " 

Used in cylinders 3981 " 

D. Efficiency of whole plant. 

At 162 lb. abs., from water at 205 deg. and with 0.006 of moisture, the heat 
of formation of one pound of steam is, 

Q = 1195.1 - 173.0 - 5.1 = 1017 B.t.u. 






238 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

The total steam rate for the plant is, 

S = 5240 4- 448 = 11.70 lb. 

Then the heat supplied per horse-power-hour is 1017 X 11.70 = 11,900 B.t.u., 
and the efficiency is, 

E = ®^ = 0.214. 
11900 

E. Effect of the auxiliaries. 

The pumps use 447 lb. of steam, which costs, as above, 1017 B.t.u. per 
pound, and return 323 lb. carrying 1140— 173 = 967 B.t.u. per pound, above 
the normal feed temperature; then the net cost is 

454,600 - 312,400 = 142,200 B.t.u. 

Per indicated horse-power of the main engine this is equivalent to 142,200 ■*■ 
448 = 318 B.t.u. per hour, so that the heat really supplied for the engine is 
11,900—318 = 11,582 B.t.u., and the efficiency of the latter becomes, 

B =ff 2 = - 220 - 

F. Limiting efficiency, of the engine alone, with the ideal feed temperature. 
In view of what is brought out in division B above, take the effective heat 

of the jacket discharge to be about 320 B.t.u. per pound (above 32 deg.), or 
250 B.t.u. above 102 deg. Per horse-power-hour, the consumption of steam by 

the engine alone is 

S = 4727 + 448 = 10.55 lb., 

of which the fraction used by the jackets is 746 -s- 4727 = 0.1578. The ideal 
feed temperature is therefore 102 + (0.158 X 250) = 141.5 deg. — see Art. (e) 
— and at 158 lb. abs., with m = 0.005, the heat of formation is, 

Q = 1194.7 - 109.5 - 4.3 = 1082 B.t.u. 

With a heat supply of 10.55 X 1082 = 11,420 B.t.u., the efficiency becomes, 

J-gg- 0.223. 

The only element that has any weight in making this E differ from the value 
0.220, found above without the auxiliaries, is the steam-pipe loss. 

(i) Heat Consumption. — The heat supply per unit of output is a 
better basis of judgment, and more directly related to thermal efficiency, 
than the steam rate. Especially, to give the amount of heat supplied 
per horse-power-hour makes the steam engine readily comparable with 
the gas engine, since that is the most commonly used measure of per- 
formance for the latter. The two output units having the values 
2545 B.t.u. for the horse-power-hour and 42.42 B.t.u. for the horse- 
power-minute, the heat rate Q is related to efficiency as shown by 
Table 11. 



§ 26 (*)] 



MEASURES OF PERFORMANCE. 



239 



Table 11. Thermal Efficiency and Heat Supply. 



Effi- 


Heat per 


Effi- 
ciency. 


Heat per 


Effi- 
ciency. 


Heat per 


ciency. 


Hour. 


Minute. 


Hour. 


Minute. 


Hour. 


Minute. 


0.05 
0.06 
0.07 
0.08 

0.09 
0.10 
0.11 


50,900 
42,420 
36,360 
31,810 

28,280 
25,450 
23,140 


848.4 
707.0 
606.0 
530.2 

471.3 
424.2 
385.6 


0.12 
0.13 
0.14 
0.15 

0.16 
0.17 
0.18 


21,210 
19,580 
18,180 
16,970 

15,910 
14,970 
14,140 


353.5 
326.3 
303.0 

282.8 

265.1 
249.5 
235.7 


0.19 
0.20 
0.21 
0.22 

0.23 
0.24 
0.25 


13,395 
12,725 
12,119 
11,568 

11,065 
10,605 
10,180 


223.3 
212.1 
202.0 
192.8 

184.4 
176.7 
169.7 



(j) Duty of Pumping Engines. — For this class of engines a 
special measure of performance is commonly used, called "duty." In 
early practice it was denned as the number of foot pounds of work 
done per 100 lb. of coal burned. Because the heating power of coal is 
a variable and uncertain quantity, this has been changed to work per 
1000 lb. of steam consumed; which is roughly equivalent to the older 
rate, since one pound of good coal will evaporate about ten pounds of 
water. For really definite comparison, the better standard is foot 
pounds of work per million B.t.u. received from the fire — this input 
quantity being derived from the thousand pounds of steam. These 
two measures are both in current use, the former often preferred for 
commercial purposes because it gives a more distinctly separate test of 
the engine and condenser. 

Duty is not determined by indicated steam work, but by the work 
of the water pistons or plungers, so that it is in terms of net work out- 
put. In some cases it has even been based upon actual water delivered, 
thus including the effect of leakage and "slip" in the pump; but the 
common practice is to credit the full work of the plungers, making or 
meeting a separate specification in regard to delivery. The effective 
pressure pumped against is got by taking the suction lift and the dis- 
charge pressure, as determined by gages near the pump, and adding 
to their sum the pressure equivalent of any difference of level between 
the gages: this credits the pump with the overcoming of all pipe resist- 
ances, in addition to the actual lift from suction level to discharge 
level, but not with work done against its own internal hydraulic resist- 
ances. 

With the million B.t.u. base, duty is readily transformed into ther- 
mal efficiency. Suppose, for example, that its value is 165 million: 






240 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

dividing out the million, we have 165 ft. lb. per one B.t.u. of heat sup- 
plied, or 165 of output per 778 of input, so that the efficiency is 

E = 165 -*- 778 = 0.2123 (139) 

For the ordinary type of Rankine-cycle engine, duty per 1000 lb. 
of steam will range higher than per 1,000,000 B.t.u., because the heat 
Q per pound of steam is likely to be in the neighborhood of 1080 B.t.u.; 
with the regenerative cycle, as described in § 27 (i), the heat-unit basis 
gives the higher value, since Q may be made less than 900 B.t.u. The 
large vertical pumping engine has a high mechanical efficiency, com- 
monly from 0.93 to 0.95, as between indicated steam power and duty 
power. Good, high values of duty, somewhat better than will be main- 
tained in regular running are 

Per million B.t.u., 165,000,000 ft. lb., and 

Per 1000 lb. of saturated steam, 180,000,000 ft. lb. 

(k) Relative Efficiency. — The ratio of actual to ideal output is 
the true criterion of the performance of an engine, when we are con- 
sidering how effectively the controllable losses are eliminated or dimin- 
ished. The logical and proper "ideal" standard is the Rankine cycle; 
various other "theoretical" diagrams have been proposed, but they 
can be rated only as makeshifts. There are, however, some draw- 
backs to the use of the relative efficiency defined by Eq. (138), due 
chiefly to wide variation in the amount of work lost through incomplete 
expansion. The example illustrated in Fig. 128 will help to make this 
matter clear. 

In that figure an assumed temperature-entropy diagram for a com- 
pound engine is shown in dotted lines. Disregarding the effect of air 
in the condenser, we take temperature to and pressure po to be in the 
steam-table relation: then, with release at 8 lb. abs., the exhaust line is 
varied from 160 deg. to 70 deg., or from 4.7 to 0.4 lb. The derived 
curves, numbered 1 to 5, are laid out on a vertical base of this exhaust 
temperature, to the enlarged scale at the right. 

Curve 1 (scale at top) shows the actual effective output W, in B.t.u., 
or the total enclosed area of the two steam diagrams, down to the 
particular exhaust line: thus for 130 deg., it is the area above DGH. 
Because the volume of the cylinder is so small relative to the specific 
volume of the steam at very low pressures, W is scarcely increased at 
all by lowering U below 100 deg. 

Curve 2 (same scale as 1) gives the Rankine-cycle output TTr, plotted 
from column 2 of Table 6, page 116. This increases with fall of to at a 
nearly constant rate. 

Curve 3 (scale at bottom) is the relative efficiency, Er = W -s- Wr. 



§ 26 (k)) 



MEASURES OF PERFORMANCE. 



241 



Its wide variation with a comparatively small change in the unit out- 
put W is what detracts a good deal from its real usefulness as a stand- 
ard of comparison. 

Curve 4 (scale along curve) shows how the heat input Q = Hi — q 
varies with changing to; on the base here used the relation is repre- 
sented by a straight line. 

Curve 5 (scale near top) gives the absolute efficiency E = W -f- Q. 
At first this ratio shows a fair rate of increase with vacuum; but it 



160 

140 

120 
to 

100 

80 







160 


200 W 1A 


^0 B.T.U. 280 


320 








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Fig. 128. — Example Showing Effect of Variant Exhaust Pressure, all other con- 
ditions remaining unchanged, including the terminal or release pressure. Initial 
pressure, pi = 120 lb. abs.; release pressure p 2 = 8 lb. abs., equivalent to 183 
deg. temperature; quality x h with effective cut-off as at p x , about 0.75; volume 
per pound at and during release, 38 cu. ft. 

reaches a maximum at about £ = 100 deg., then begins to decrease 
slowly. 

The engine diagram in Fig. 128 is typical in its proportions, es- 
pecially as to the terminal condition of the steam, at point D — see 
§ 15 (g) for a statement of the considerations which limit the amount 
of practically advantageous expansion. The unfairness of the relative 
efficiency, represented in curve 3, as a basis of comparison among 
engines is apparent from the fact that an engine with a poor vacuum 
may show a better relative performance than another which is work- 
ing with a good vacuum, doing more work per pound of steam, and de- 



242 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



veloping a higher absolute efficiency. To overcome this difficulty, it 
has been proposed to stop the adiabatic expansion, in the ideal engine, 
at a terminal pressure equal to that in the actual engine, then drop to 
the exhaust pressure by cooling at constant volume — in strict his- 
torical accuracy, this modified scheme is the reference cycle favored by 
Rankine, while Clausius preferred to adhere to the cycle with full ex- 
pansion. The objection to this plan is that the introduction of another 
condition makes the ideal operation less definite and determinate, the 
calculation of its output becoming more troublesome and complicated. 
Further, for the steam turbine, which is under no such volumetric re- 
striction as the engine, the full-expansion diagram represents decidedly 
the amount of available work: in the capability of utilizing the triangu- 
lar area under the curve DEG, Fig. 128, the turbine has its one really 
strong point of thermodynamic superiority over the engine. 

(I) A Simple Relative Standard. — The trouble with the scheme 
leading to curve 3, Fig. 128, is that a change in exhaust pressure 
which has a great effect upon the output of the ideal cycle can pro- 
duce but a small change in the output of the actual engine. Since 
practical limitations of cylinder volume thus greatly diminish tfye 



Table 12. Rankine-cycle Output T^r, Expressed in B.t.u., Per 
Pound of Steam Initially Dry-saturated. 

Lower Limits, 
For noncondensing engines, p = 15 lb. abs., t = 213 deg. 
For condensing engines, p = 1.94 lb., t = 125 deg. 





Output. 




Output. 




Output. 


Pi 






Pi 






V\ 








Atm. 


Vac. 




Atm. 


Vac. 




Atm. 


Vac. 


250 


203.8 


316.8 


150 


167.8 


284.4 


75 


117.7 


239.2 


240 


201.0 


314.3 


140 


162.8 


279.9 


70 


112.7 


234.7 


230 


198.0 


311.6 


130 


157.5 


275.1 


65 


107.3 


229.8 


220 


194.9 


308.8 


120 


151.8 


269.9 


60 


101.4 


224.5 


210 


191.6 


305.9 


110 


145.5 


264.3 


55 


95.0 


218.7 


200 


188.2 


302.8 


100 


138.5 


258.0 


50 


88.1 


212.4 


190 


184.6 


299.5 


95 


134.8 


254.7 


45 


80.4 


205.0 


180 


180.8 


296.0 


90 


130.9 


251.1 


40 


71.9 


197.7 


170 


176.7 


292.4 


85 


126.8 


247.4 


35 


62.4 


198.2 


160 


172.4 


288.6 


80 


122.4 


243.4 


30 


51.9 


179.8 



influence of variation in back pressure, the latter almost ceases to be a 
major determinant of real performance. In view of this fact, a simple 
and convenient standard of reference may be established by choosing 



§ 26 (/)] MEASURES OF PERFORMANCE. 243 

mean or typical values of exhaust pressure, for the respective cases of 
noncondensing and condensing engines, then calculating the Rankine- 
cycle outputs with these lower limits, as was done in preparing Table 
12. The choice must be somewhat arbitrary (in the mathematical 
sense of the word) : the values here used, specified in the heading of the 
table, are taken as a little better than the average of really good prac- 
tice, looking rather at the back pressure upon the piston than at the 
pressure in the condenser. When comparison is made with an ideal 
performance taken from this table, excessive back pressure will simply 
be bunched with the other sources of loss. For many purposes, such 
a comparison, beside being easy to make, will be more satisfactory than 
one with the result of the relatively exact calculation outlined in Exam- 
ple 15, page 105: the latter "standard " is used, however, in Table 13. 
(m) Economical Vacuum. — As already noted concerning the 
typical example in Fig. 128, the absolute efficiency shown by curve 5 
has its maximum at about 100 deg., while there is practically no gain 
below 125 deg. The assumption which underlies this curve — namely, 
that the back pressure on the piston corresponds (as for pure steam) to 
the temperature in the condenser, which temperature is retained by 
the water of condensation — is at once simpler and more favorable to 
high vacuum than is the actual state of affairs. Because of air in the 
condenser, always present to some extent, the pressure there is higher 
than that corresponding to the temperature; and from condenser to 
engine there is the added back pressure due to pipe and port resist- 
ances. In a given engine, with fixed sizes of ports, etc., the difference 
between the exhaust pressure in the cylinder and the ideal condenser 
pressure will decrease somewhat as the latter is made lower, but in 
much less than direct proportion; so that it will have a relatively greater 
harmful effect as the vacuum is increased. This will swing the lower 
part of curve 1 toward the left, raising the maximum on curve 5. 

The limit of commercial efficiency is farther up the scale of exhaust 
pressure than that fixed by purely thermodynamic considerations. To 
get the very high vacua which are found profitable in steam-turbine 
practice requires a larger and more expensive condenser outfit than can 
be made profitable with the engine; and if the supply of cooling water is 
I at all limited, it will not pay to use an excessive amount. To main- 
' tain an absolute pressure of 0.75 lb. in the condenser will probably 
cost twice as much, in apparatus and water, as to maintain 1.5 lb.; 
while 1.5 lb. will cost very little more than 3 lb. The turbine can 
realize a large proportion of the ideal gain from the higher vacuum, 
the engine but a small fraction of it. Plant conditions are so varied 
that no closely quantitative generalization is warranted; but, roughly, 



244 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

to make the vacuum greater than 27 inches of mercury, or the absolute 
condenser pressure less than 1.5 lb., will not produce any net gain in a 
steam-engine plant. Further description and discussion of condenser 
action will be found in Chapter XL 

(ri) Equivalent Steam Rates. — In expressing performance by 
the steam rate, it is quite customary to reduce actual consumption to 
equivalent dry steam. This is done on the basis of equal heat content, 
above the initial temperature of heat reception (generally the feed- 
water temperature). Suppose, for instance, that steam at 120 lb. abs., 
from water at 180 deg., contains 2 per cent of moisture. The heat 
of formation of dry steam, with this pi and to, will be 1189.8 — 127.8 = 
1062.0 B.t.u., and that of the wet steam, 1062.0 - 17.6 = 1044.4 
B.t.u. Then one pound of the latter will be equivalent to 1044.4 -j- 
1062.0 = 0.9843 lb. of the former. If the engine uses 15.6 lb. of steam 
per horse-power-hour, the equivalent dry steam will be 15.6 X 0.9843 = 
15.36 lb. With superheated steam, the rate number will be increased 
by reduction to the equivalent at dry saturation. 

Frequently, instead of getting the heat-bearing equivalent, testing 
engineers simply subtract the weight of the moisture from the total 
steam coming to the engine, and call the result the dry steam supplied. 
This is not a scientific procedure, but has certain practical points in its 
favor. For one thing, so far as the performance of the engine is con- 
cerned, the harm done by the entrained water in augmenting cylinder 
losses will far exceed any possible gain from its heat content. Under 
the quite common proviso that " commercially dry steam " is to be 
supplied, it may be said that if moisture is not removed by an efficient 
separator, the very least concession is not to charge the engine with 
any heat which it may carry. On the whole, however, it is better to go 
to the heat-unit basis, emphasizing thermodynamic efficiency rather 
than mere steam rate, and perhaps giving more commercial importance 
to relative efficiency. Above all, the character of any change from 
actual to equivalent or adjusted quantity should be clearly stated in 
the report of a test, especially if it is a departure from common prac- 
tice, or if more than one usage is generally accepted. 

§ 27. Examples of Performance 

(a) Scope of Presentation. — The examples now to be set forth, 
together with those already given in § 22, cover the whole range of 
steam-engine practice, as will appear from a glance at the columns for 
size, speed, limiting pressures, etc., in Table 13. For graphicalillustra- 
tion, the simple pressure-volume diagram is chosen, in preference to 



§ 27 (a)] EXAMPLES OF PERFORMANCE. 245 

any derivative from it, such as the temperature-entropy diagram. In 
every case, the direct indicator diagrams are replotted so that the per- 
formance of one pound of steam is represented, according to the scheme 
of § 21 (I). In Table 13, numerical values of data and of calculated 
results are arranged in systematic fashion, and from its columns a clear 
idea of the magnitude of the various quantities can readily be gotten. 
All of the diagram examples are included in the table, together with 
some others that have not been thus illustrated. 

(6) Scheme of the Steam Diagrams. — In regard to the combined 
or transformed diagrams in Figs. 129 to 140, the following points are 
to be noted: 

All are laid out to the same scale of pressures and, with one or two 
exceptions, to the same scale of volumes: these have been chosen with 
regard to the space available on the page, and are used also for the 
simple-engine diagrams in Figs. 90, 92, 98, 99, and 109. Adherence to 
these established scales leads to marked distortion of form in some 
extreme cases, such as Figs. 133 and 134; but this is more than bal- 
anced, for present purposes, by the advantage of ready comparability. 

Without exception, the scheme of combination is that of the full- 
line diagrams in Fig. 80, the clearance lines or axes of zero volume being 
brought to a common position. 

Where the clearance effects are large, in Figs. 134 and 135, hyper- 
bolas touching the expansion and compression curves of the respective 
diagrams are carried down or up to horizontal, intermediate reference 
lines, for a graphical comparison of the volume measures of the work- 
ing steam — compare the slightly different scheme in Fig. 80. In 
every case, relative values of the net pv product, for selected points, are 
given under the letter M (standing for " measure")- From the total 
value of pv, at a point on the expansion curve, is subtracted the value 
for the clearance steam, from a point on the compression curve. The 
net pv at high-pressure cut-off or for the high-pressure cylinder is 
taken as unity, and the other values are expressed in terms of this 
unit. 

Under the letter D (for " division ") are given sets of ratios or frac- 
tions which show how the work per cycle or the power developed is 
divided among the cylinders or stages. 

Regularly, the diagram is drawn for one pound of working steam, 
fed to the cylinder, or for more than one pound of total steam consumed 
in a jacketed engine. Exceptions, in which the jacket steam is included 
within the pound, are found in Fig. 135, where the jacket water was not 
measured, in Fig. 136, where there is a special purpose of comparing 
performance without and with jackets, and in Fig. 140, where the jacket 



246 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI 

water could not have been drained off without deranging the cycle. 
The reference curve drawn outside the expansion curves is the satura- 
tion line, for one pound of steam, laid out from column 2 of Table II; 
and the extra curve, of which just the beginning is dotted in on Figs. 
129, 130, and 131, shows what would be the added volume of the steam 
condensed in the jackets. 

Since the expansion curve represents the volume of all the steam in 
the cylinder, including the clearance steam, the missing quantity is not 
given directly by the distance between that curve and the saturation 




Cu. Ft. 



Fig. 129. — Direct-expansion Engine with No Receiver. Holly duplex compound 
pumping engine, 21 and 42 by 36 in., ratio 4.04, r.p.m. 20, full jackets. Engine 
at South Bethlehem, Pa., test by author in 1902. No. 34 in Table 13. 

line: but its volume is shown, very approximately, by the difference 
between the intercepted width of the diagram and the abscissa of the 
one-pound curve. The comparison would be made more" striking by 
transforming the diagrams so as to bring their compression curves to 
the line of zero volume, as in the dotted-line case of Fig. 80 and in Fig. 
81 ; but the extra labor and the added confusion of lines on the reduced 
illustrations are good reasons for omitting this step. 

On the single diagrams in Fig. 133, the saturation curves SS are 
drawn for the whole weight of steam expanding in the cylinder and the 
missing quantity is directly shown. This is feasible where there is but 
one cylinder, so that the quantity of clearance steam does not change, 
and where several diagrams are not referred to the same axes, as is 
done in Figs. 134, 136, etc. 

Each diagram here given is at least the mean of a full set of indicator 
cards; with a duplex engine, as in Figs. 129, 133, 134 II, and 137, this 



§27 (6)]" EXAMPLES OF PERFORMANCE. 247 

signifies that four sets of ordinates have been measured and averaged. 
In some cases the combined diagrams are the mean of a number of 
sets of indicator diagrams, representing the whole of a long test. 

The essential facts about the engine are given beneath the figures. 
Other information, with derived results as to performance, will be 
found in Table 13. 

(c) Engines w t ith Small Compression. — In Figs. 129, 130, and 
131 are given diagrams which show a minimum of departure or loss 
from the simple, "ideal" form of Fig. 57 and Fig. 76. They are all 
from pumping engines, necessarily slow-running: the low speed makes 
the kinetic losses small, while permitting small ports and low clearance 
ratios; at the same time, its possible harmful effect in the direction of 
cylinder losses is neutralized by the influence of steam jackets and 
reheating receivers. The diagrams are well filled out, or the diagram 
factor, as defined in § 29 (6), is high. 

Figure 129 does not represent especially good performance, but is 
chosen to illustrate the type of compound engine with absolutely no 
receiver. The two pistons are coupled together through a vertical 
rocker beam, as outlined above the diagram; the strokes are simul- 
taneous and opposite, and a single valve between the cylinders (at each 
end) controls high-pressure exhaust and low-pressure admission. The 
low-pressure diagram is drawn in three different ways: first, at A, it is 
placed beneath the high-pressure diagram, on the same base line (com- 
pare Fig. 77), chiefly in order to show how nearly the two lines of com- 
mon expansion agree; next, at B, it is stretched out to the full length 
representing the volume of the low-pressure cylinder, as in all the 
other figures; finally, at C, the length is made equal to the increase of 
volume during the common expansion. At the beginning of the stroke, 
the communicating volume comprises the high-pressure cylinder V\ and 
the two clearances; diagram C begins at this distance from the vertical 
axis, and its length is (V 2 — Vi). Evidently, this last scheme gives the 
best test of the continuity of expansion. As regards the representation 
of work, it will be noted that areas A and C are together equal to area 
B; the simplest interpretation of the diagrams is to think of the low- 
pressure piston area A 2 as divided into two portions, A\ the same as the 
small piston, and (A 2 — Ai). The former receives the work of diagram 
A, the latter that of C. Only in the particular case of no expansion in 
the low-pressure cylinder alone is there need or use for this expedient. 

Figure 130 shows a performance of higher excellence. The combined 
effect of low speed and full jacketing is seen in the unusually marked 
reevaporation toward the end of the high-pressure expansion, and in 
the increase of the pv measure; reference to Table 13 will show an 



248 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



unusual increase in the indicated steam from initial cut-off to final 
release. The mechanism connecting the two pistons is essentially the 
same as in the preceding engine, although different in its arrangement 







Cu.Ft. 



Fig. 130. — Direct-expansion Engine with a Receiver. Leavitt vertical compound 
beam-fly-wheel pumping engine at Louisville, 27 and 54 by 120 in., ratio 4.02, 
r.p.m. 18.6, full jackets and reheater. F. W. Dean, 1894, Trans. A. S. M. E., 
Vol. 16, page 169. No. 35 in Table 13. 

and proportions, and there is a receiver of considerable size between the 
cylinders. 

The standard type of pumping engine for large water works is now 
the vertical triple-expansion. From the highest development of the 
compound, in Fig. 130, to an early example of the triple, in Fig. 131 I, 
is a very short step. Between I and II the chief difference is ah in- 
crease of steam pressure from about 120 to 150 lb. by gage. The ex- 
cellence of these diagrams is patent, and they call for no comment. 
To supplement the data in Table 13, extending them to performance in 
the pump cylinder, the results in the tabulation on the next page are 
added. The water horse-power is calculated from the effective pres- 
sure pumped against, which is measured by gages, as explained in 
§ 26 (j), so that the mechanical efficiency E m includes the effect of some 



§ 27 (c)] 



EXAMPLES OF PERFORMANCE. 



249 




Fig. 131. — Two Vertical Triple-expansion Pumping Engines, with jackets and 

reheaters. 

I. Allis-Chalmers Engine at Milwaukee, 28, 48, and 74 by 60 in., ratio 7.11, 
r.p.m. 20.3 R. C. Carpenter, 1893, Trans. A. S. M. E., Vol. 15, page 313, also En- 
gineering Record, Dec. 2, 1893, No. 36 in Table 13. 

II. Snow Engine at Indianapolis, 29, 52, and 80 by 60 in., ratio 7.66, r.p.m. 
21.2. W. F. M. Goss, 1898, Trans. A. S. M. E., Vol. 21, page 793. No. 37 in 
Table 13. 



Results from Pumping Engines. 





Figure. 


Steam 
horse- 
power. 


Water 
horse- 
power. 


Mech. 
efficiency 


Steam per hour, 


Duty per 1000 
lb. steam. 


Table 13. 


Steam 
horse- 
power. 


Water 
horse- 
power. 


34 
35 
36 
37 

(a) 


129 
130 
131 I 
131 II 


281 
643 
574 
783 
866 
926 


246 
599 
518 
735 

823 
879 


0.921 

0.931 

0.902 

0.938 

0.95 

0.95 


15.63 
12.22 
11.80 
11.50 
10.31 
9.65 


16.97 
13.22 
13.07 
12.26 
10.86 
10.15 


116,700,000 
149,700,000 
151,100,000 
161,600,000 
182,400,000 


38 




195,000,000 












250 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



hydraulic friction. The duty here given is per thousand pounds of 
steam; to get that per million B.t.u., apply E m to the absolute thermal 
efficiency E in Table 13, then reverse the calculation shown in Eq. 
(139). On this latter basis, 165 million at the plungers, or 175 million 
at the steam pistons, is about the limit of performance of the engine 
working on the Rankine cycle. 

The test marked (a), not given in Table 13, is from a Holly engine 
at Philadelphia, 30, 60, and 90 by 66 in., at 20.1 r.p.m., with steam at 
180 lb. by gage, carrying 0.0114 of moisture: the values in italics are 
based on an assumed 0.95 efficiency. Test of March, 1910, from Bulle- 
tin of Holly Manufacturing Co. In test 38, the steam is superheated. 




Fig. 132. — Mean Indicator Diagrams (four cylinder ends), from simple locomo- 
tive, 21 by 30 in., No. 2 in Pennsylvania Railroad Tests at St. Louis Ex- 
position, as listed under Fig. 103. 

(d) Engines with Large Compression. — This class is in strongest 
contrast with that just considered. The large clearance which is 
implied results partly from using wide ports, in adaptation to high 
speed, partly from the use of a single valve, requiring long ports; while 
long compression is an unavoidable accompaniment of early cut-off, 
with a single valve, as is shown by the typical diagrams in Fig. 132 — see 
also § 39. The class embraces the small, high-speed, automatic cut-off 
engine, represented by Figs. 2, 5, and 7, the locomotive, and the marine 
engine. 

The general type of diagram from the stationary, high-speed engine 
is sufficiently illustrated in Figs. 84 and 78. Several diagrams from a 
simple locomotive, the engine with the greatest range of pressure in a 
single cylinder, are given in Fig. 132 and are transformed to our uniform 
system in Fig. 133. Thus replotted, they show clearly in what part of 
the whole range of expansion the locomotive has its field of operation, 
and how well that field is covered. To test the conformity of the ex- 
pansion curve to the hyperbola pv = C, a short piece of the latter, as 
produced from cut-off at C, is drawn outside the release R in tests 6 
and 8; in test 5 it falls right on the expansion curve at R. 

The performance of the compound locomotive is represented by 



§ 27 (d)] 



EXAMPLES OF PERFORMANCE. 



251 



200- 



150- 



100- 



50 



No. 5 



AU 
97.2 



i i i i I i i 



103.7 




v 5 Cu.Ft. 10 5 5 

Fig. 133. — Diagrams in Fig. 132, on "unit" system, with same scales as other 
figures in this Section. Volumes for one pound of working steam, but steam 
curves SS for total steam expanding, including clearance steam. Weights as 
follows: 



Test. 



Cut-off. 



Steam weight. 



5 0.173 1.250 

6 0.307 1.147 
8 0.407 1.110 

These three tests are averaged together as No. 6 in Table 13. 



Fig. 134. The clearance effects are large, especially in case B of figure I, 
where the high-pressure diagram is shoved out more than half-way be- 
yond the one-pound saturation curve. We have here a striking example 



252 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

of the influence of speed upon steam distribution; as noted beneath the 
diagrams, the cut-offs (by the valve) are nearly the same in cases A 
and B ; but at the higher speed the pressure at cut-off is so much lowered 
by valve and port throttling, and the pressure at compression is so much 






D 

A B 

.628 .725 

.372 .275 



B 

1.000 
.940 




: 



Cu.Ft. 10 



Fig. 134. — Diagrams from Compound Locomotives, Pennsylvania Railroad Tests, 

St. Louis, 1904. 

I. Cross-compound (two-cylinder), Consolidation type, 23 and 35 by 32 in., 
ratio 2.34: No. 3 under Fig. 103, No. 7 in Table 13. Diagram A, test 308 (in origi- 
nal report), r.p.m. 80, cut-off 0.53; B, test 312, r.p.m. 160, cut-off 0.50. 

II. Four-cylinder, Atlantic type, 14.2 and 23.7 by 25.2 in., ratio 2.81: No. 5 
under Fig. 103, No. 8 in Table 13. Diagram A, test 508, r.p.m. 160, cut-off 0.50; 
B, test 512, r.p.m. 240, cut-off 0.34. 



I 



§ 27 (d)] 



EXAMPLES OF PERFORMANCE. 



253 



raised, that the relative amount of clearance steam is more than doubled. 
In II the receiver pressure is abnormally low, with the result of ex- 




CuFt. 



Fig. 135. — Triple-expansion Marine Engines, Tests by Committee of the Insti- 
tution of Mechanical Engineers. 

I. Steamship Meteor: 29, 44, and 70 by 48 in., ratio 5.70, r.p.m. 72, jackets on 
all cylinders. Proc. I. M. E., 1889, and Engineering, 1889 I, page 527. No. 11 
in Table 13. 

II. Steamship Iona: 22, 34, and 57 in. by 39 in., ratio 6.75, r.p.m. 61, jacket 
on high-pressure cylinder only.} Proc. I. M. E. 1891, and Engineering, 1891 I, 
page 568. No. 12 in Table 13. 

cessive drop loss in case A. Besides large clearance effects, the charac- 
teristics of these diagrams are large kinetic losses and high back pres- 
sure — the last due to the exhaust nozzle, and an inherent element in 
the operation of the locomotive. Locomotive performance is repre- 
sented by tests 6 to 10 in Table 13: in spite of the losses just named 
and of the strong cylinder action shown in Fig. 105, quite a fair relative 
efficiency (compared with the Rankine cycle) is realized. 

The diagrams in Fig. 135 are typical of the marine engine, although 
they are from rather small ships, and with not very high steam pres- 
sures: in some lines of service, pressures of 250 lb. by gage are common. 
Comparatively few steam-consumption tests of marine engines have 



254 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

been made: the difficulties are greater than on land, and the simple 
coal test of the whole plant is generally considered enough. Diagram 
II shows an unusually long expansion: total contained volumes of 25 
to 35 cu. ft. per pound of steam (including clearance) are usual, as 
against 50 cu. ft. and more in Figs. 130 and 131. This short expansion 
and the large kinetic losses and compression effects account for the 
comparatively high steam rates of marine engines. In tests 11, 12, 
and 13 of Table 13, $h ranges from 13 to 15 lb. In warship engines 
more closely designed as to size of cylinders, 15 to 16 lb. is the com- 
mon range of steam consumption — see data collected in Table 75D of 
Steam Engine, Vol. II. In the poor relative efficiency of the marine 
engine is seen the reason why the turbine surpasses it in economy: as 
against good stationary engines, the turbine has no great advantage in 
thermodynamic performance, except in the better utilization of vacuum. 

(e) Comparisons of Steam Action. — We now take up power gen- 
erating engines of the Corliss class — this name of the most prominent 
member being given to the whole class of engines which have the same 
general kind of steam distribution: they are characterized by small 
clearance and compression, but in the matter of kinetic losses lie be- 
tween the low-speed pumping engine and the slide-valve type. The 
first two examples, brought together in Fig. 136, present a most in- 
structive comparison between the systems of nonuse and use of steam 
j ackets — each engine being properly designed for its particular con- 
ditions. In A we have a large engine at fairly high speed, the com- 
bination of size and speed being such that jacketing would have little, 
if any, useful effect : the engine had a reheater in the receiver, but even 
that was left out of action during the tests. In B, on the other hand, 
the engine is smaller, the speed is low, and the ratio of expansion is 
somewhat greater; jackets are fully applied, to barrels and heads of 
the cylinders, and to the receiver. Note that diagram B is drawn for 
one pound of total steam consumed, the jacket steam being included 
under the one-pound saturation curve. For the cylinder feed alone, 
the constant-weight curve (of which the beginning is dotted in) would 
be laid out for 0.881 lb., since the jackets use 0.119 of the steam 
supplied. 

Above the steam diagrams are given quality diagrams for the two 
cylinders, showing the ratio of indicated to actual steam weight in the 
cylinder during expansion: these are on a stroke-line base, instead of 
the pressure base in Fig. 82 and in Fig. 138. The relative heights of 
the high (H) and low (L) quality curves in the respective cases are 
typical: the uhjacketed engine shows a decrease in the steam fraction 
x from first to second cylinder, the jacketed engine an increase; and 



§ 27 (e)] 



EXAMPLES OF PERFORMANCE. 



255 



the resulting increase in the work of the low-pressure stage is the prin- 
cipal gain from jacketing. The different ways in which the product 
pv changes (as indicated under M) are also typical: it falls off much 
more rapidly without the jacket. 

Between these two engines there is a balancing of gains and losses 
which leads to almost an equality in thermal efficiency — see Table 
13. Engine A has slightly superheated steam and realizes a much 











I- 


H 






















^ 


^ 


^ 








»-' 

















L 

s 

— X. 

. ' . ■ 



.8 1.0 




A 




B 


1.000 


1 


1.000 


1.050 


2 


1.021 


.865 


3 


.910 


.852 


4 


.943 



Fig. 136. — Comparison of Corliss Engines Without and With Jackets. 

A. Horizontal, cross-compound, plain receiver, no jackets, cylinders 30 and 
56 by 72 in., ratio 3.48, r.p.m. 65. J. E. Denton and others, 1893, Trans. A. S. M. E., 
Vol. 15, Page 882. No. 24 in Table 13. 

B. Compound beam engine, reheater, full jackets, cylinders 17 and 34 by 60 
in., ratio 4.09, r.p.m. 34. M. Longridge, 1895, Engineering, 1895 I, page 132. No. 
25 in Table 13. 

fuller steam volume, especially in the high-pressure cylinder; B has the 
advantage of higher initial pressure and longer expansion, and shows 
smaller kinetic losses between the stages. If the two were brought to 
common limits of action (initial pressure and final volume), the situa- 
tion would be summed up by saying that in engine B the special heat- 
ing devices do not quite succeed in overcoming the handicap of smaller 
size and lower speed. 



256 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



The example in Fig. 137 has no direct bearing on the preceding 
comparison, except that, in a very large engine at good speed, it shows 
high steam quality without the use of any auxiliary heating devices. 
The principal interest lies in the change from ordinary condensing 



200-1 r-l m 



150- 



100— 



50- 

La 
Abs." 



fifiT-? 




v 



i 1 r~ 

10 CuFt. 20 



30 



40 



Fig. 137. — Large Corliss Engine Driving Electric Generator. Duplex, cylinders 
42 and 86 by 60 in., ratio 4.30, r.p.m. 75, neither jackets nor reheater. Inter- 
borough Power House, New York City: H. G. Stott, Jour. A. S. M. E., Mar. 
1910, Vol. 32, pages 315 to 372. No. 27 in Table 13. 

operation, test A, to what is essentially noncondensing action, tests 
B and C; this change permitting a low-pressure turbine to be placed in 
series with the engine. Reference to Table 13 will make it evident 
that we have here a striking illustration of the matter discussed in § 26 
(7c). The relative efficiency Er is only 0.60 with vacuum exhaust; but 
when the exhaust pressure is raised the engine is able to realize from 









§ 27 (e)] 



EXAMPLES OF PERFORMANCE. 



257 



0.75 to 0.80 of the ideally possible performance, in spite of the large 
kinetic losses so apparent in the combined diagrams. Smallness of the 
missing quantity, together with a fairly large proportion of clearance 
steam, causes the high-pressure expansion curves to lie well outside of 
the one-pound volume curve, and brings those of the low-pressure 
cylinder quite close to that curve. Along with work-division D is given 
the work A U per pound of steam, found from the diagram by planim- 
eter and expressed in B.t.u. : that these values do not quite agree with 
those under W in Table 13 is due in part to unavoidable inaccuracy in re- 
drawing Fig. 137 from published diagrams, and perhaps also to the orig- 
inal use of indicator cards which were not quite the average for the run. 
(/) Effect of Jackets and Reheatees. — In regard to the eco- 
nomical effect of these devices, examples can be found which range all 



0.2 m Q 0.6 0.4 0.2 m o 




Fig. 138. — Quality at Critical Points, Compound Engines of Corliss or equivalent 
types, Barms' Engine Tests : original numbers used to designate tests. 

Group I. No jackets or reheaters. 
Group II. Reheaters only. 

Group III. Jackets and reheaters: No. 47 not included in means. 
Group IV. Same engines, with and without jackets and reheater (full and 
dotted lines respectively). No. 38 is added as an example of excessive leakage. 

the way from 20 per cent gain to nearly 10 per cent loss, using steam 
per horse-power-hour as the basis of comparison; but the omission of 
exceptional cases will cut these limits down to about plus 10 and minus 
3 per cent. The only such pair of tests in Table 13, No. 29, shows a 
slightly greater consumption with the jackets, which is just balanced 
by the gain in feed temperature. Partly as further information along 
this line, partly to show how erratic are the data available, a number of 
results from engines working under service conditions are diagrammed 
in Fig. 138, on the scheme of Fig. 105. The " quality " shown is the 



258 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

ratio of indicated steam to actual steam consumed: since clearance 
steam is not included, the fraction represented is not quite the true 
quality of the steam in the cylinder; further, the jacket steam here 
forms a part of the " missing quantity." In the first three groups, 
average points are found and marked by blacked circles; also, results 
from Eq. (126), for the missing steam at initial cut-off, are indicated 
by + marks: the values of mt are laid off directly in group I, but in II 
and III they are measured (after proper reduction) to the left of first 
+ marks which show the proportion of steam used in jackets and 
heater — except that in two tests of group III the latter quantity was 
not found. These comparisons have interest in connection with the 
last columns on page C of Table 13. 

Comparing means in groups I to III, we note practically the same 
realized volume at the initial cut-off in all three cases, but decidedly 
stronger reevaporation in the first cylinder with the jackets in action. 
From I to II there is a good gain in quality in the lower stage, hardly 
maintained in III. Group IV contains two pairs of comparative tests, 
'each pair from the same engine under different conditions, and agrees 
with Fig. 136 in showing better quality in the high cylinder without 
the jackets, in the low cylinder with them. Test 38 is put in merely 
to show how greatly the missing quantity may be increased by leakage. 

Experience in the use of these heating devices can be summed up 
in the simple statement that with large engines, at good speeds and 
well loaded, their effect is nearly neutral, although generally inclined to 
the side of a small gain. As the conditions of operation are more con- 
ducive to cylinder losses, jackets are more beneficial: thus a jacket 
system which produces very little net benefit at full load, and causes a 
loss at overload, will quite strongly promote economy under a light 
load, with its excessive ratios of expansion. The old Michigan test, 
Fig. 92 and No. 18 in Table 13, is a case where very decided improve- 
ment would have resulted from the use of a steam jacket. 

The function of the reheater is to furnish dry, and preferably super- 
heated steam to the low-pressure cylinder. A thoroughly sound view 
of the principles involved is embodied in the scheme, applied in some 
of the best-designed engines, of passing the exhaust from the higher 
cylinder through a regular " steam separator," thus removing most of 
the contained water mechanically, and then sending it over the heat- 
ing surface. The expenditure of live steam to evaporate water into 
steam which can at best work through but a part of the whole tempera- 
ture range, is not a logical and effective device for increasing economy. 

(g) Effect of Superheating. — A small or poorly placed super- 
heater, or a long and poorly insulated steam pipe, may give only the 






§ 27 (g)] EXAMPLES OF PERFORMANCE. 259 

slight superheats of 10 to 15 deg. seen in several of the tests in Table 13 : 
this amounts to little more than furnishing dry steam and throwing in 
a little extra heat for good measure. With the superheater incorporated 
into the construction and into the hot-gas circulation of the boiler, 
there is a moderate range, say from 50 to 150 deg. above saturation. 
Very high superheats, approaching the limit of about 400 deg., and 
involving steam temperatures as great as 750 deg., are usually and 
most safely produced in separately-fired superheaters. To avoid over- 
heating of the tubes, the supply of heat to their surface must be more 
closely and carefully regulated when it is being abstracted by a current 
of hot steam than when a body of relatively and definitely cooler water 
is present; such regulation is more difficult when the superheater is a 
part of the main boiler, and if it is placed too near the fire there is 
serious danger of its being " burned out " when the boiler is forced. 

The proper basis of judgment upon the thermal economy of super- 
heating is found, not in the steam rate, but in the thermal efficiencies, 
both absolute and relative. Referring to Figs. 55 and 56, we readily 
see that if the engine can maintain the relative efficiency Er undimin- 
ished as superheat is added, there will be some gain in absolute E, be- 
cause the ideal performance is better when a part of the heat is received 
at temperatures above that of saturation; if Er increases, yet more 
advantage will be gained. Consider the example diagrammed in Fig. 
139 and entered as No. 30 in Table 13. Comparing superheated steam 
at 737 deg. with saturated steam at 362 deg., we see steam consumptions 
in the ratio of 100 to 145: in the thermal quantities, letting 100 repre- 
sent the value with common steam, the relative numbers with super- 
heated steam are : 

Heat supplied per pound of steam 119 

Output of Rankine cycle 129 

Actual output 145 

Absolute efficiency 122 

Relative efficiency 112 

These do not quite correspond with the results in Table 13, because 
they are got by referring both tests to an exhaust pressure of 2 lb. 
abs., according to the scheme of Table 12, page 242. The most im- 
portant showing is the 22 per cent gain in absolute efficiency. This is 
unusually high for an engine of the naturally economical type, gains of 
6 to 12 per cent being more common. The greatest improvement has 
been found in certain small, simple engines. As an instance may be 
quoted some tests made by Professor Ripper and reported in Proc. 
Inst. C. E., 1896, Vol. 128, page 60: the engine was a 7 by 12 in. Schmidt 



260 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

superheat " motor," run noncondensing at 180 r.p.m. : with steam at 
130 lb. abs. and superheated about 330 deg., the consumption per 
horse-power-hour was 17 to 18 lb., while with saturated steam, dropped 
to 100 lb. abs., the consumption rose to 38 lb. There is strong reason 
to believe that the saving of steam in such engines is in large measure 
due to a diminution of leakage — compare the valve leakage described 
in § 22 (p), which is of a kind that would be greatly reduced by super- 
heating. 

Against the large saving in steam consumption, typically repre- 
sented by. tests 10 and 30 to 33 in Table 13, and the smaller yet con- 
siderable gain in thermal efficiency, certain disadvantages must be 
charged. One is the more rapid deterioration of the superheater, as 
compared with the boiler, because of excessive temperature of the 
metal. This causes trouble in piping and in engine also, as affecting 
the material to some degree, and as making necessary greater allow- 
ance and freedom for expansion and contraction. Lubrication of the 
valves and piston is more difficult with superheated steam : at one time 
in the history of the engine, this was a principal influence leading to the 
abandonment of superheating; when it was revived, beginning in the 
early 1890's, better lubricants were available, in the way of high-grade 
mineral oils. Now the cylinder lubrication of a steam engine with 
high superheat is certainly no more difficult than that of the large gas 
engine. 

(h) Performance with High Superheat. — This is well exempli- 
fied by Fig. 139, where comparative tests from the same engine are 
laid out on the same one-pound basis. A separately-fired Schmidt 
superheater produced the high temperature noted ; as already remarked, 
this type of apparatus has the advantage of controllability, but the 
economic disadvantage that the standby loss, or the amount of coal that 
must be used for banking the fire overnight, will probably be relatively 
greater than in the larger furnace of the boiler. A portion of the main 
steam supply was shunted through the reheater, then turned back 
into the current. The engine had lift or poppet valves in the high- 
pressure cylinder, Corliss valves in the low. In spite of the cooling 
effect of the reheater coil and of the cylinder walls, the steam is quite 
strongly superheated at high-pressure cut-off, and somewhat super- 
heated at release ; and after reheating it is still above saturation during 
the first part of the low-pressure expansion. That the heat inter- 
changes are small is shown by the close approach of the expansion 
curve to the adiabatic form : thus if the coordinates of points 1 and 2 of 
diagram A are substituted in the equation piVi n = p2Vz n , the value 
of n is found to be 1.26 for a curve which will pass through these 



§ 27 (h)] 



EXAMPLES OF PERFORMANCE. 



261 



points; while for a true adiabatic n would be a little over 1.3 — see 
§ 14 (e). 

This marked change in the form of expansion exerts quite an in- 
fluence upon the division of work between the cylinders, as is shown 
both by the numbers under D and by the indicator diagrams, which 
represent practically the same development of power. The specific 



150 




Fig. 139. — Compound Engine with Highly Superheated Steam. Horizontal, cross- 
compound, reheater, no jackets; 16 and 28 by 42 in., ratio 3.08, r.p.m. 102; test 
A with steam superheated 375 deg., test B with saturated steam. D. S. Jacobus, 
1903, Trans. A. S. M. E., Vol. 25, page 264. No. 30 in Table 13. 

steam volumes are relatively so much smaller in the lower stage when 
working from high superheat that the cylinder ratio is less for the same 
completeness of expansion (as measured by the pressure at release). 
The three to one ratio in this engine is about equivalent in effect to a 
four to one ratio with saturated steam. 

(i) The Regenerative Cycle. — An actual example of the scheme 
outlined in Fig. 59 is given in Fig. 140. The feed water, drawn from a 
hot-well tank, first passes through a surface heater in the exhaust line, 
between the low-pressure cylinder and the condenser; it then goes 
through a series of four mixing heaters, being pumped from each lower 
one into the next, in which there is a higher pressure and temperature. 



262 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



Steam for these heaters is taken from the low-pressure cylinder at 
release (intermittently, through a special valve), and from the third, 
the second, and the first receivers — the jacket and reheater drains 



200 







CuIFt. lb 



Fig. 140. — Engine with Regenerative Feed Heaters. Nordberg quadruple engine 
at Pittsburg; cylinder sizes given on diagram, ratio 9.08, r.p.m. 36.5, jackets 
and reheaters. R. C. Carpenter, 1898, Eng. Record, Apr. 22, 1899; also R. H. 
Thurston, Trans. A. S. M. E., Vol. 21, page 203. No. 39 in Table 13. 'Compare 
Fig. 141, page 273. 

being included in the steam and water thus abstracted from the work- 
ing cycle. The last heater delivered water at 311 deg., as compared 
with a steam temperature of 388 deg. in the boiler; while with the 
similar engine listed as No. 40 in Table 13, the feed temperature was 
334.5 deg. and that of the steam 403.5 deg. 

The normal working of the engine is represented by the full-line 






§ 27 (i)] EXAMPLES OF PERFORMANCE. 263 

diagrams in Fig. 140. The relative decrease in effective volume as the 
pressure falls, due to the diminution in the quantity of steam passing 
through the cylinders, is clearly shown, graphically by comparison 
with the dotted diagrams, numerically by the ratios under M for case 
A. The main plot is made for one pound of total steam consumed, 
since that used in the jackets could not well be determined, except by 
inference from thermal changes. The diagrams in dotted line are laid 
out on the same base line, or for the same power, hence do not repre- 
sent the working of one pound of steam; they show performance with- 
out the special feed heaters, but with the jackets still in action. 

The ideal output and the relative efficiency for engines of this class, 
Nos. 39 and 40 in Table 13, are based on the Carnot cycle efficiency, as 
in Eqs. (96) and (97). Decidedly, steam per horse-power-hour is not 
the proper criterion of performance when comparing tests like Nos. 38.2 
and 39, where there is a difference of 25 per cent in S& but practical 
equality in thermal efficiency. Any jacketed engine in which the 
jacket water is either returned to the boiler at full pressure or mixed 
with the feed water so as to raise the latter above the exhaust tempera- 
ture goes a little way from the Rankine cycle toward the regenerative, 
form, but not far enough to call for any change toward the Carnot basis 
of comparison. 

(j) Scheme and Showing of Table 13. — The various classes of 
engines represented are indicated by the division titles on page B. 
The table includes all the engines of which steam diagrams have been 
given in this section, many of those represented by the steam-con- 
sumption diagrams in § 22, and others selected to fill out the illus- 
tration of typical performance. It must be borne in mind that the re- 
sults here shown are, in most cases, somewhat better than the average 
working of engines of the several classes. Special tests, of sufficient 
importance to be fully published, are generally made when the engine 
is comparatively new and in good condition, with a minimum of leak- 
age; and there is a natural tendency for poor results to be suppressed 
rather than to get into print. 

The notation of the table will now be described and defined, with 
some remarks as to the range of variation of the more important quan- 
tities. To facilitate comparison with reports in the metric-centigrade 
system, the reduction ratios of the differing units are given beneath the 
definitions. 

When comparing these engine-test results with those from turbines, 
as given in Table 20, it must be borne in mind that here indicated 
power is the measure of output, there shaft or brake power. For 
machine efficiency of the engine, see § 28, following. 



264 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. \ 

Page A. Condition of Operation, Sizes of Cylinders, Speed and 

Expansion Data. 

No. — A serial number is given to each engine; decimal figures desig- 
nate different tests of the same engine. 
Condition. — By a condensed notation a number of important general 
conditions of the test are stated, as follows: 
First letter — condition of steam : 
T = saturated steam; 
P = superheated steam. 
Second letter — kind of exhaust : 

A = atmospheric exhaust, or noncondensing; 
C = condenser or vacuum exhaust. 
Numeral — number of stages in the expansion. 
Third and fourth letters — condition as to jackets and heaters: 
J = jackets in use; 
H = reheater in receiver in use; 
N = no jackets or heaters. 

If either J or H is given alone, absence of the other type of 
heating device is implied. 

Last letter — manner of measuring steam consumption : 
F = feed water weighed or measured; 
M= feed water metered; 
C = steam condensed and weighed. 
N Speed in revolutions or double strokes per minute. 

V Piston speed in feet per minute — see § 3 (d). 

(1 meter per sec. = 196.7 ft. per min.) 

e Apparent cut-off in high-pressure cylinder, or fraction of stroke 

completed at cut-off, not counting the clearance. 

r Ratio of expansion, or ratio of the final full volume of the low- 

pressure cylinder to the volume back of the high-pressure piston 
at cut-off, clearance being taken into account. If R is the 
cylinder ratio and i\ and i 2 the clearances as given above, 

r = R (1 +>> (140) 

Here the cut-off ratio e is measured at a pressure below that of 
admission, so that the expansion ratio r does not show quite the 
full range from the effective initial volume (as at H, Fig. 73) to 
the final volume in the low-pressure cylinder. The latter show- 
ing is preferable, but in some cases the pressure at cut-off was 
not given. 






§ 27 0)] EXAMPLES OF PERFORMANCE. 265 

Diameters. These, with the clearances given on page B, fix the essential 
Stroke. dimensions of the engine as regards steam action. 

Ratio. The Ratio (R in Eq. 140) lies between mean piston areas 

or piston displacements in the low-pressure and the high-pres- 
sure cylinders, passing over the intermediates in a triple or 
quadruple engine. Some discussion of cylinder ratios will be 
found in § 29 (i). Note the one case of two cylinders in a 
stage, in No. 33, which is a four-cylinder triple, having two low- 
pressure cylinders in " parallel." 

Page B. Clearances, References, Etc. 

Clearances. These are mean values for the first and last cylinders, 
expressed in the usual fashion as fractions of the displacement 
or nominal cylinder volume. Note the extreme range from 0.18 
in locomotive No. 9 to less than 0.01 in pumping engines Nos. 
36 and 39. These exceedingly low values are secured by using 
single-disc lift valves in the low-pressure cylinder, as against 
Corliss valves in the higher cylinders. 

References. In many cases it will be necessary to go back to one of 
the steam diagrams to get a full reference. The principal 
sources, covering all but five of the American tests, are the 
book Engine Tests, by G. H. Barrus, the book of Locomotive 
Tests and Exhibits, by the Pennsylvania Railroad Company 
at the St. Louis Exposition of 1904, and the Transactions of the 
American Society of Mechanical Engineers. But a few Euro- 
pean tests are included in this table. The more extensive tables 
in Steam Engine, Vol. II, cover a wider range. 

Page C. Steam Conditions, Power, and Steam Consumption. 

m Fraction of moisture in steam received by engine. 

s Degrees fahrenheit of superheat, at engine when so given in 

original report, otherwise at superheater. 
Pi Absolute steam pressure, in pounds per square inch. This 

should be measured in the steam pipe, just above the shut-off 

valve at the engine; in some of the tests it was taken at the 

boiler only. 

(1 kg. per sq. cm. = 14.22 lb. per sq. in.) 

p Absolute exhaust pressure, reduced to pounds per square inch, 

as explained in § 12 (b). Marked E, this is pressure in the 
cylinder, from the indicator diagram; marked C, it is in the 
condenser or the atmosphere : see also t Q , page 267. 






266 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

p m Mean effective pressure, reduced to the low-pressure piston in 

all multiple -expansion engines — see § 21 (g). 
H Indicated horse-power. 

(1 metric h.p. = 0.9863 English h.p. — see § 26 (a). 
$h Steam per horse-power-hour, in pounds : this is the actual steam 

consumption, not corrected for moisture or superheat as de- 
scribed in § 26 in). It includes all steam used in jackets or 
reheaters. Compare summary in § 26 (6). 
(1 kg. per met. h.p. = 2.235 lb. per Eng. h.p.) 

j The fraction of the total steam supplied to the engine that is 

used in the jackets and reheaters. A blank in this column 
indicates the absence of the quantity from the test. 

$i c Indicated steam at initial cut-off, in same terms as S^, calcu- 

lated by the methods in § 21 (/) and (g) — compare also the 
steam quantities described in § 21 (k). 

S{ T Indicated steam at final release, similar in terms to jSj c . 

m Fraction of the steam entering the cylinder, or of S^ (1 — j), 

which is not shown by the indicator diagram, representing the 
difference between this cylinder feed and the i.s.c. S[ c . Only 
where j is unknown and represented by a (?) does this " missing 
fraction " include the jacket steam. 

raf Missing-steam fraction calculated from the initial-condensation 

formula, Eq. (126), for comparison with actual m c . In the large- 
compression group, tests 1 to 12, m f does not come directly 
from the formula, but is increased in the ratio of total steam to 
working steam, as is done in § 22 (k), for Fig. 103. 

Taking m f as a standard of comparison, the following points may 
be noted, in brief supplement to and summary of the full presentation 
and discussion of data in § 22 : 

The formula is properly applicable to engines without jackets, and 
with not more than a beginning of superheating. In the small-com- 
pression class, engines 14 to 18, 20, 21, and 27 come under this definition; 
and with the exception of tests 15.1, 16.1, and 27.2, the discrepancy 
between m c and m f lies within 3 or 4 per cent of the steam supplied to 
the cylinder. The large-compression engines, Nos. 1 to 12, show far 
wider differences, especially the compounds, this being in accord with 
what is set forth in § 22 (I) and (m); see also the discussion of com- 
pression in § 23. 

Cases and causes of m c being much too large relative to ra f are, 
tests 11 and 19, jacket steam included; test 23, leakage; test 40, ex- 
cessively wet steam. For the rest, m c is consistently smaller than m t 



§ 27 0) EXAMPLES OF PERFORMANCE. 267 

with jackets, but not in any such regular fashion as to suggest a formu- 
lable relation. With high superheat, comparison would be wholly 
illogical — consider Fig. 139. 

Some useful comparisons between m c and m f are made in Fig. 138. 

Page D. Thermodynamic Performance. 

t Temperature of exhaust, corresponding to the exhaust pressure 

outside the engine, or to p when marked C in the table. 
From t can be got, by the use of Table I, the condenser pres- 
sure upon which it is based, when this is not directly given. 
Note that with all the noncondensing engines, t is taken as 
for the existing pressure of the atmosphere, the engine per- 
formance * suffering the full effect of back pressure. Compare 
§ 26 (e) as to this and the following item. 

q Heat in one pound of feed water, at ideal feed temperature, 

which is higher than t with a jacketed engine. Without jackets 
or reheaters, q is (to — 32) ; in a few cases it is so taken with 
jackets; but generally the engine is credited with the heat 
returned to the feed by the water from the jackets. The 
question of ideal and actual feed temperatures is considered in 
§ 26 (d) and (e). Only in tests 38, 39, and 40 are actual, plant 
values of q here given. 

hi Total heat of one pound of steam at pressure pi and of the 

quality fixed by m or s. 

h 2 Total heat at the end of adiabatic expansion from pi to p — 

see § 15 (d) for this calculation for the Rankine cycle. 

Q equal to (hi — q ), is the input of heat per pound of steam, or 

the heat of formation at pi and m or s, above the state of 
water with q . 

TFr equal to (hi — h 2 ) is the output of the Rankine cycle, as in 
§ 15 (d). For the regenerative cycle, tests 39 and 40, the Carnot 
cycle efficiency is entered instead of h 2 , then under W R is given 
the output that would result from this efficiency with the actual 
input Q — not quite the same as by Eq. (97). 

W Actual work output per pound of steam, expressed in B.t.u. 

It is equal to (2545 -s- S h ), as in § 26 (c), Eq. (136). 

E Absolute thermodynamic efficiency, equal to (W -f- Q), as in 

Eq. (137) — compare the summary in § 26 (c). 

E R Relative efficiency (W 4- W R ), as in Eq. (138)— see § 26 (c) 
and (k). 

Q m Heat supplied per i.h.p. per minute, equal to (42.4 -J- E) — see 
§ 26 (t). 



268 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



Table 13, page A. 



Tests of Various 



No. 


Condition. 


N 


V 


e 


r 


Diameters X Stroke. 


Ratio. 


1 

2 
3 

4 
5 

6 

7 

8 

9 

10 

11 
12 
13 


TAINF 
TAINF 
TAINF 
TA2NF 
TC2NF 

TAINF 
TA2NF 
TA2NF 
TA2NF 
PA2NF 

TC3JF 
TC3JF 
TC4NC 


308 
354 
246 
293 
299 

80 

80 

160 

240 

240 

72 
61 

78 


719 
531 
533 
635 

648 

400 
427 
632 
1037 
942 

574 
398 
700 


.31 
.28 
.12 
.39 
.38 

.30 
.55 
.44 
.50 
.40 

.50 
.37 


2.5 

2.2 
5.0 
6.3 
6.4 

2.8 
3.5 
5.4 
4.4 
5.3 

9.9 
14,7 


8 X14 

9.5 X 9 

14.5 X13 

11.5,18.5 X13 * 

11.5,18.5 X13 

21 X30 
23, 35 X32 
14.2,23.7 X25.2 
15, 25 X26 
14.2,26.1 X23.6 

29.4, 44, 70 X48 
22, 34, 57 X39 
29,41.5,59,84 X54 


2.61 
2.61 

2.34 
2.81 
2.81 
2.46 

5.70 
6.75 
8.45 










14.1 
2 
3 
4 

15.1 
2 
3 

16.1 
2 

17.1 
2 

18 


TA1NC 

TAINF 

2 
3 

TAINF 

C 
PA1NF 

C 

TC1NF 


88 

86 
8.6 

62 
406 
401 
405 

51 

52 
153 
155 

13.7 


438 
430 
43 
309 
406 
401 
405 

505 
520 
612 
620 
219 


.21 
.11 

.15 
.47 
.22 
.31 
.61 

.22 
.12 
.34 
.26 
.30 


3.8 
5.9 
4.9 
1.9 
3.8 
5.0 
5.9 

4.1 
6.9 
2.9 
3.6 
3.0 


17 X30 

14 X 6 

10, 14 X 6 

7, 10, 14 X 6 

28 X60 
17 X24 
36 X96 


1.97 
4.10 


19 
20 
21 

22.1 
2 
23 

24 

25 

26 

27.1 
2 
3 


PC2JF 
PC2HF 
TC2HF 
PC2JHM 

PC2JHC 

PC2NM 

TC2JHC 

TC2JHF 

PC2NC 

TA2NC 


70 

77 

75 

100 

100 

102 

65 
34 
121 
75 
75 
75 


700 
767 
752 
928 
935 
816 

783 
340 
844 
750 
750 
750 


.24 
.31 
.33 
.29 
.11 
.21 

.30 

.17 
.25 
.21 
.40 
.60 


12.0 
11.5 
11.9 
14.4 
33.1 
18.9 

11.1 
19.9 
15.0 
18.4 
9.2 
7.8 


28, 48 X60 

28, 54 X60 
28,56 X60 

29, 60 X56 

23, 48 X48 

30, 56 X72 
17, 34 X60 
20, 40 X42 
42, 86 X60 


3.04 
3.69 
4.06 
4.33 

4.38 

3.48 
4.18 
4.03 
4.30 


28 
29.1 
2 

30.1 
2 
31 
32 
33.1 


TC2JHF 
PC2NF 
JH 

PC2HF 

T 

PC2HC 

TC3NF 

TC3JHF 

P 


61 
80 
80 

102 

102 

101 

76 

83 
83 


726 
641 
641 

716 
715 
604 
608 
703 
703 


.26 
.29 
.24 

.32 

.27 
.20 
.30 


22.8 
20.6 
24.5 

9.3 
10.7 
11.6 
22.0 


18, 44 X72 
16, 40 X48 

16, 28 X42 

21, 36 X36 

19, 29, 46 X48 
34, 49, 61-61 X51 


6.40 
6.35 

3.13 

2.98 
6.00 
6.40 


2 
















34 
35 
36 
37 
38.1 


TC2JF 

TC2JHF 

TC3JHF 

TC3JHC 

TC3JHC 

P 

TC4JHC 
TC4JHC 


20.2 
18.6 
20.3 
21.2 
24.1 
24.0 

36.5 
56.9 


121 
372 
203 
212 
241 
240 

255 

455 


.42 
.20 
.35 
.33 


9.1 

20.2 
19.6 
22.6 


21, 42 X 36 

27, 54 X120 

28, 48, 74 X 60 

29, 52, 80 X 60 

30, 56.5, 84 X 60 

19.5, 29, 49.5, 57.5X42 
14.5, 22, 38, 54 X48 


4.04 
4.02 
7.11 

7.66 

7.85 


2 

39 
40 


.52 
.62 


16.9 
22.4 


8.75 
14.19 



§ 27 (j)] 



EXAMPLES OF PERFORMANCE. 



269 



Steam Engines. 




Table 13, page B. 


No. 


Clearances. References, etc. 


Fig. 




ENGINES WITH LARGE COMPRESSION. 

SMALL HIGH-SPEED ENGINES. 




1 
2 
3 
4 
5 


.14 

.141 

.10 
.07 .10 
.07 .10 


No. 23b ) 
16b 
13 
42b 
41bJ 


-From Engine Tests, G. H. Barrus. 





LOCOMOTIVES. 



.093 



.057 


.098 


.066 


.114 



Nos. 



205, 6, 8 
308, 9 
507, 8 
609, 10, 11 
709, 10, 11 J 



Penn. Railroad Tests, St. 

Louis Exposition of 1904. 
See Fig. 103. Mean of two 

or three tests in each case. 



133 
134 I 
134 II 



MARINE ENGINES. 



124 
124 



.080 
.076 



S. S. Meteor ) Comm. Inst. M. E., see refer- 

S. S. Iona ) ence Fig. 135. 

S. S. Saxonia Engineering, 1902 I, 326 



1351 
135 II 



ENGINES WITH SMALL COMPRESSION. 

SIMPLE ENGINES AND SPECIAL TESTS. 



14 


.071 


Denton and Jacobus tests, Figs. 86, 90, 98. 


86 


15 


.125 .105 .058 


Willans tests, first series, see Fig. 96. 


96 


16 


.03 


No. 20b and a ) From Engine Tests, G. H. 
10b and a ( Barrus. 




17 


.02 




18 


.058 


Isherwood, S. S. Michigan, see Figs. 91, 92. 


91 



COMPOUNDS, CORLISS, AND EQUIVALENT TYPES. 



19 
20 
21 

22 
23 

24 
25 
26 
27 


.025 

.04 

.031 

.028 

.02 

.026 
.035 
.047 
.098 


.025 

.06 

.043 

.04 

.03 

.036 
.027 
.070 
.048 


No. 43 ) 

48b / From Engine Tests, G. H. Barrus. 

55 ) 
L. S. Marks ) Engs. C to F, 4 tests at full load. 
See Fig. 97 ( Eng. B, 2 tests at full load. 

J. E. Denton, Trans. A. S. M. E., 15-882. 
M. Longridge, Engineering, 1896 I, 132 
D. S. Jacobus, see Fig. 88. 
H. G. Stott, Jour. A. S. M. E., Mar., 1910. 


97 

136 A 
136 B 

88 
137 



HIGH-RATIO COMPOUNDS. 



.023 
.025 



.018 
.020 



No. 47b, c, d, Barrus' Engine Tests. 

G. H. Barrus, Eng. Record, 1902 II, 436. 



HIGH-SUPERHEAT AND TRIPLE-EXPANSION ENGINES. 



30 


.041 


.058 


D. S. Jacobus, Trans. A. S. M. E., 25-264. 


139 


31 


.087 


.094 


M. Longridge, Engineer, 1905 I, 546. 




32 


.03 


.03 


Engineering, 1894 II, 230 




33 


.03 


.03 


Zeit. Ver. d. Ing., 1900, 606. 





PUMPING ENGINES. 



34 


.036 


.025 


R. C. H. Heck, 


129 


35 


.016 


.015 


F. W. Dean, Trans. A. S. M. E., 16-169, 


130 


36 


.014 


.008 


R. C. Carpenter, Eng. Record, 1893, Dec. 2. 


1311 


37 


.017 


.025 


W. F. M. Goss, Trans. A. S. M. E., 21-793. 


131 II 


38 






Bull. Holly Mfg. Co., Engine at Louisville, 
1909. 





ENGINES WITH REGENERATIVE HEATERS. 



.013 
.060 



.004 
.035 



R. C. Carpenter, Eng. Record, 1899 I, 495. 

O. P. Hood, Trans. A. S. M. E., 28-705; air 

compressor, Michigan copper mine, 1906. 



140 



270 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



Table 13, page C. 










Tests < 


df Various 


No. 


TO, S, 


V\ 


Po 


Pm 


H 


s b 


3 


Sic 


■A 


TO 


TO f 


1 

2 
3 
4 
5 

6 

7 

8 

9 

10 

11 
12 
13 




.03 
.01 
.004 
.004 

.005 
.016 
.012 
.013 
91° 

.015 
.015 
.015 


97 
107 
117 
143 
145 

216 
223 

218 
222 
203 

153 
180 
207 


15. 5e 
15. Oe 
15.5b 
16.0e 
3.6e 

18. 6e 
19.4e 
18.7e 
21.4e 
17.8e 

2.7c 
0.7c 
2.3c 


34.9 
30.8 
20.1 
30.3 
37.6 

91.4 
79.8 
49.5 
49.7 
33.0 

29.9 
21.1 

38.8 


32 

35 

53 

153 

197 

757 

987 

877 

1528 

719 

1994 

645 

9099 


31.20 
32.99 
32.67 
25.20 
19.10 

25.12 
19.86 
20.14 
20.43 
17.61 

14.98 
13.35 
13.47 


? 

.043 


22.5 
21.5 
17.7 
15.6 
12.0 

18.7 
16.8 
15.5 
15.3 
15.0 

11.6 

8.9 


21.8 
22.9 
22.6 
16.7 
12.8 

19.2 
15.3 
15.0 
14.6 
14.8 

11.3 
8.3 


~.280 

.348 
.461 
.383 
.371 

.257 
.150 
.233 
.249 
.148 

.229 
.335 


.24 
.25 
.32 
.16 
.18 

.232 
.127 
.179 
.128 
.217 

.135 
.217 














14.1 
2 
3 
4 

15.1 
2 
3 

16.1 
2 

17.1 
2 

18 


.01 
.01 
.01 
.01 
.01 
.01 
.01 

.012 

.012 

41° 

16° 

.015 


105 

106 

109 

43 

106 
159 

187 

80 
83 
90 
95 
36 


14.4c 
14.4c 
14.4c 
14.4c 
14.7c 
14.7c 
14.7c 

16.2e 
3.6e 

15. 7e 
4.6e 

2.2c 


40.9 
26.2 
42.2 
19.2 
38.9 
46.0 
45.0 

23.8 
23.1 
36.8 
39.4 
19.9 


119 
75 
12 
39 
34 
40 
40 

452 
444 
310 
336 
134 


26.47 
27.97 
38.67 
45.29 
26.00 
19.19 
18.70 

30; 16 

23.00 
25.64 
20.51 
35.20 




20.6 
18.9 
16.7 
36.8 
18.3 
15.9 
16.6 

21.8 
14.1 
20.8 
15.8 
18.3 


21.6 
24.3 
22.4 
38.5 
20.4 
15.4 
15.9 

23.2 
14.4 
20.4 
15.5 

20.4 


.223 
.324 
.568 
.188 
.296 
.172 
.112 

.278 
.385 
.189 
.229 
.296 


.248 
.320 
.591 
.192 
.232 
.150 
.085 

.246 
.358 
.200 
.244 
.323 


19 
20 
21 
22 
23 

24 
25 

26 

27.1 
2 
3 


44° 
13° 
.005 
86° 
15° 

14° 



.007 

9° 

.013 

.010 


135 
136 

166 
177 
171 

138 
149 
163 
190 
199 
195 


2.5e 
4.0e 
3.2e 
2.3e 
1.9e 

2.1c 
0.5c 
1.0c 
0.94c 
16.1c 
12.1c 


26.1 
23.9 
30.7 
28.4 
24.1 

25.6 
23.3 

26.7 
26.0 
27.7 
37.7 


1017 
1252 
1714 
2220 
1075 

1592 
216 
853 
6846 
7261 
9904 


13.26 
14.01 
13.27 
11.91 
13.59 

13.50 
13.05 
12.33 
12.59 
18.06 
16.13 


? 
.040 
.035 
.066 
.070 

.119 
.099 


10.1 
11.2 

10.8 

10.0 

8.4 

11.8 
10.0 
9.4 
10.4 
14.6 
14.1 


10.2 
11.6 
10.8 
10.4 
11.6 

11.4 
11.6 

12.6 
13.6 
15.3 


.238 

.169 

.153 

.08 

.33 

.125 
.235 
.16 

.176 

.188 
.118 


.188 
.161 
.138 
.161 
.194 

.179 

.358 

.19 

.136 

.098 

.093 


28 
29.1 
2 

30.1 


.006 
41° 
41° 

375° 
.01 
398° 
.01 

213° 


166 
186 
184 

157 
160 
132 

178 
218 
213 


2.1c 
0.9c 
1.2c 

1.5c 
2.3c 
1.0c 
2.3e 
1.1c 
1.1c 


20.5 
23.3 
23.3 

31.8 
30.8 
22.5 
25.8 
25.2 
24.1 


692 
567 
566 

420 
407 
415 
785 
2976 
2850 


12.67 
11.29 
11.49 

9.56 
13.84 

9.00 
11.75 
11.75 

9.62 


.077 

.135 


? 

6 


9.2 
10.0 

8.7 


9.6 
8.5 
8.6 


.195 
.114 
.124 


.198 
.206 
.222 


2 




31 
32 


(Mean of tests 1 and 3) 


33.1 


? 
? 




2 








34 
35 
36 
37 

38 1 


.009 
.006 
.011 
.010 
.029 
110° 

.013 
.057 


97 
152 
136 
169 
•174 
170 

214 

257 


2.0c 

1.0c 

1.2c 

1.6c 

1.16c 

1.16c 

1.2c 
1.3c 


27.7 
25.0 
21.7 
24.4 
23.9 
23.6 

35.4 
31.3 


281 
643 
574 

783 
940 
926 

712 
990 


15.63 
12.22 
11.80 
11.50 
10.82 
9.65 

12.42 
11.92 


.123 
.167 
.093 
.062 
.075 
.048 

.165 
.103 


11.9 

7.8 
9.4 

8.7 


13.1 
9.7 
9.0 
9.3 


.130 
.233 
.128 
.195 


.292 
.338 
.228 
.226 


2 










39 

40 


9.7 
9.3 


7.9 
7.0 


.065 
.133 


.103 
.099 



Italic figures mean values assumed by author. 



§ 27 0') 



EXAMPLES OF PERFORMANCE. 



271 





Steam Engines — Continued. 


Table 13, page D. 


No. 


k 


Qo 


h 


h 2 


Q 


^R 


w 


E 


Er 


Q m 


1 


212 


180 


1177 


1041 


997 


135.9 


81.0 


.081 


.596 


523 


2 


212 


180 


1161 


1020 


981 


140.8 


77.2 


.079 


.548 


539 


3 


212 


180 


1181 


1031 


1001 


149.9 


77.9 


.078 


.520 


545 


4 


212 


180 


1189 


1024 


1009 


164.9 


101.0 


.100 


.613 


424 


5 


130 


98 


1190 


915 


1092 


274.3 


133.2 


.122 


.486 


348 


6 


211 


179 


1200 


1004 


1021 


196.0 


101.3 


.098 


.517 


432 


7 


211 


179 


1200 


1002 


1021 


198.2 


128.1 


.125 


.646 


339 


8 


211 


179 


1200 


1003 


1021 


196.5 


126.3 


.124 


.643 


344 


9 


211 


179 


1200 


1002 


1021 


198.1 


124.6 


.122 


.628 


348 


10 


211 


179 


1254 


1049 


1075 


204.8 


144.4 


.134 


.707 


316 


11 


138 


121 


1181 


917 


1060 


264.3 


170.0 


.160 


.643 


265 


12 


90 


70 


1184 


844 


1114 


340.1 


190.7 


.171 


.560 


248 


13 


132 


100 


1187 


895 


1087 


291.5 


189.0 


.174 


.649 


244 


14.1 


211 


179 


1179 


1035 


1000 


143.5 


96.2 


.096 


.671 


442 


2 


211 


179 


1179 


1035 


1000 


142.1 


91.0 


.091 


.640 


466 


3 


211 


179 


1179 


1033 


1000 


146.0 


65.8 


.066 


.451 


645 


4 


211 


179 


1161 


1082 


982 


79.1 


56.3 


.057- 


.711 


741 


15.1 


212 


180 


1179 


1036 


999 


142.8 


97.9 


.098 


.686 


433 


2 


212 


180 


1186 


1014 


1006 


171.8 


132.6 


.132 


.722 


322 


3 


212 


180 


1189 


1006 


1009 


183.0 


136.1 


.135 


.745 


314 


16.1 


212 


180 


1171 


1049 


991 


122.3 


84.4 


.085 


.690 


498 


2 


146 


114 


1172 


959 


1058 


213.5 


110.6 


.105 


.518 


406 


17.1 


212 


180 


1207 


1045 


1027 


162.3 


99.3 


.097 


.611 


439 


2 


143 


111 


1195 


968 


1084 


226.5 


124.1 


.114 


.549 


371 


18 


130 


98 


1153 


972 


1055 


180.6 


72.4 


.069 


.401 


619 


19 


128 


96 


1218 


941 


1122 


277.7 


192.0 


.171 


.691 


248 


20 


114 


92 


1200 


934 


1108 


266.2 


181.6 


.164 


.682 


259 


21 


116 


93 


1191 


889 


1098 


302.3 


191.9 


.175 


.635 


243 


22 


130 


114 


1248 


947 


1134 


300.9 


213.8 


.189 


.711 


225 


23 


109 


95 


1204 


890 


1109 


314.1 


187.5 


.169 


.597 


251 


24 


128 


96 


1201 


867 


1105 


277.6 


188.5 


.170 


.679 


249 


25 


80 


80 


1194 


845 


1114 


348.5 


196.3 


.176 


.563 


240 


26 


102 


96 


1189 


868 


1093 


321.1 


206.4 


.184 


.625 


231 


27.1 


100 


68 


1204 


868 


1137 


336.4 


202.3 


.178 


.601 


238 


2 


217 


185 


1187 


1007 


1003 


180.1 


140.9 


.140 


.768 


302 


3 


202 


170 


1190 


992 


1020 


198.0 


157.7 


.155 


.797 


274 


28 


120 


106 


1190 


895 


1084 


295.5 


201.0. 


.186 


.683 


229 


29.1 


99 


67 


1224 


895 


1157 


329.2 


225.6 


.195 


.685 


217 


2 


108 


112 


1226 


893 


1114 


330.4 


221.5 


.199 


.670 


214 


30.1 


116 


84 


1391 


1008 


1307 


382.3 


266.2 


.204 


.697 


208 


2 


132 


100 


1186 


910 


1086 


276.6 


183.7 


.169 


.665 


250 


31 


105 


73 


1393 


1004 


1320 


389.1 


282.8 


.214 


.727 


198 


32 


102 


70 


1188 


864 


1118 


324.5 


216.6 


.194 


.667 


219 


33.1 


105 


93 


1200 


864 


1107 


336.2 


216.5 


.196 


.644 


217 


2 


105 


98 


1319 


937 


1221 


382.6 


264.6 


.217 


.693 


196 


34 


126 


110 


1177 


932 


1067 


245.2 


162.8 


.153 


.664 


278 


35 


102 


112 


1190 


870 


1078 


316.3 


208.3 


.194 


.659 


219 


36 


108 


88 


1183 


872 


1095 


299.0 


215.7 


.197 


.721 


215 


37 


118 


120 


1187 


909 


1067 


299.3 


221.3 


.207 


.739 


205 


38.1 


107 


89* 


1171 


860 


1082 


311.6 


235.1 


.217 


.755 


195 


2 


107 


93* 


1260 


920 


1166 


340.1 


263.8 


.226 


.775 


187 


39 


107 


281* 


1189 


(.326) 


908 


296 


204.8 


.226 


.693 


188 


40 


110 


305* 


1155 


(.334) 


850 


284 


213.5 


.252 


.753 


168 



* From actual feed temperatures. 



272 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI, 

Note that the ideal output W-& is determined for the actual exhaust 
pressure (and temperature), not for an assumed mean as suggested in 
§ 26 (I) : the resulting erratic variation in Er is strikingly apparent in 
the comparison of test 12 with 11 and 13, and of 25 with 24. The 
paired tests 5-6, 16, and 17, with 27, show how much more effectively the 
engine can utilize theoretically available steam work in the range above 
atmosphere than in the range of low pressures and large specific vol- 
umes — compare § 26 (A;) and (m). Tests 6 to 10 enforce this idea, for 
even with the large kinetic and other losses shown in Figs. 133 and 134, 
the locomotive has almost as good a relative efficiency as have the high- 
grade, multiple-expansion, condensing engines. 

(k) Diagrams of Plant Performance. — A very good way of 
showing the distribution of heat in a steam plant is exemplified in Fig. 
141. This graphical heat balance is called the Sankey diagram, having 
been devised by Captain H. R. Sankey and first described in the Re- 
port of the Committee of the Institution of Civil Engineers, " On the 
Thermal Efficiency of Steam Engines," in 1898. 

The scheme is so self-evident and the representation so luminous 
that no description or explanation seems to be called for. The small 
difference between 100 per cent of heat received and 22 per cent of 
work plus 75 per cent of heat rejected to the condenser is the sum of 
all the radiation losses: these are represented by single lines curving off 
from the main stream at each section of the apparatus. 

In order to correlate the working of the combined boiler and engine 
plant with the general ideas set forth in § 10, the temperature-entropy 
diagrams in Fig. 142 have been laid out. Probable and typical pro- 
portions are assumed, and to make the example less abstract, numerical 
values are given in the description which follows. The drawing is purely 
illustrative, however, the method not lending itself to exact representa- 
tion of plant action : to get closely determinative data for the heat curve 
BHE would be almost impossible. 

The first diagram, ABEF, shows in simplified fashion the action of 
the products of combustion in serving as an intermediary between the 
thermo-chemical operation of heat generation and the purely physical 
absorption of heat by the water in the boiler. The assumed data are, 
a calorific power of 14,000 B.t.u.. an evaporation of 10 lb. of water, and 
20 lb. of hot gases, all per pound of combustible. Then per pound of 
steam made we have two pounds of chimney gases and 1400 B.t.u. of 
heat generated. 

Starting at 530 deg. abs., point B, and using a constant specific heat 
of 0.24 for the gases, the impartation of 1400 B.t.u. under constant 
pressure would raise the temperature by 1400 -f(2X 0.24) = 2920 



§ 27 (fc)] 



EXAMPLES OF PERFORMANCE. 



273 



deg., or to the ideal height 3450 deg. Actually, because the specific 
heat increases with the temperature, and because some heat is radiated 



r^15.e# - HEAT SUPPLIED JACKETS 




Fig. 141. — Diagram of Heat Distribution, for test A in Fig. 140. From Professor 
Thurston's paper, Trans. A. S. M. E., Vol. 21, page 216. 



274 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 
3500-1 



3000- 



2500- 




Fig. 142 



G F MS 

Temperature-entropy Diagram for the Whole Plant. 






from the incandescent fuel and flame directly to the boiler surfaces, 
the resultant effect is as if the gases received heat according to some 
such curve as BHE: 2700 deg. abs. is a good, high furnace temperature, 
only exceeded with strong forced draft. Of course, this curve by no 
means shows the real detail of the very complex heat interchanges. 
Curve BC is got with the help of Eq. (48), and the area ABEF is then 
made equal to that under BC. 



1 



§ 27 (k)] EXAMPLES OF PERFORMANCE. 275 

As the hot gases circulate over the heating surfaces, they give up 
heat, and may be thought of as cooling along the curve EH. At .some 
terminal temperature GH this heat surrender will cease, and the prod- 
ucts of combustion will go to the chimney. The residual temperature 
of 1200 deg. abs. is rather high, but the residual heat HGAB is only 22.2 
per cent of the heat of combustion : for simplicity, all the losses in the 
boiler are lumped together as heat carried off to the chimney. The 
absorption of the heat GHEF, 1100 B.t.u. in amount, is the next thing 
to be considered. 

Assuming a strong regenerative action by the jackets of the engine 
— compare the concluding paragraph of Art. (i) — the feed tempera- 
ture is taken as 150 deg., against an exhaust temperature of 100 deg.; 
then GJ is 610 deg. abs. Evaporation takes place at 366 deg. or about 
165 lb. abs., and a little superheating is produced by the 1100 B.t.u. 
imparted. The ideal output QJKLNQ is about 326 B.t.u., which 
would give an absolute efficiency of 0.296; assuming an actual efficiency 
of 0.215, the relative ratio E R is 0.726, so that 0.274 X 326 = 89 B.t.u. 
of the theoretically available heat fails to be converted into work. The 
line TU (not at all a line of operation) divides off this amount; and 
added to the heat rejected at the exhaust temperature, it augments the 
latter by the amount MNRS. 

The main purpose in drawing this diagram is to show how increase 
of entropy from heat source to heat receiver is a measure of incurred 
waste. In the fire and hot gases as source, heat GHEF is carried by 
the small entropy GF, and only the area QF is below the level of thermo- 
dynamic activity. In the highly irreversible impartation of heat to 
the relatively cool water, there is the great increase of entropy from 
GF to GM, and the unusable heat grows from QF to QM. Imperfec- 
tions of the engine cause the further addition NS. 

The cycle diagram of the gas engine lies along a curve analogous to 
BE, but its vertical width is kept comparatively small by the fact that 
the exhaust curve is of generally similar form to BE: in other words, 
there is no such uniform low temperature of heat rejection as with the 
steam engine. 

§ 28. Friction and Machine Efficiency 

(a) Various Conditions as to Output. — In § 3 (a) the various 
kinds of load that an engine may carry have been briefly described. 
To the class of " power " engines, with rotary load, the term brake 
horse-power — see § 19 (n) and § 26 (a) — is most directly and exactly 
applicable: the work against friction, which absorbs a part of the indi- 



276 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

cated work of the steam upon the piston, belongs strictly to the engine 
itself. This is essentially true even with a direct-connected electric 
generator, for if the magnetic field of the latter be not excited its rotor 
is nothing more than a part of the fly-wheel mass of the engine; and 
the combined unit has practically no more friction of shaft bearings 
than the engine alone would have. With small and moderate-sized 
engines, the real output can be directly measured, by means of some 
form of brake or absorption dynamometer. With electrical loading, 
the output of the generator is readily known; and if the losses in the 
generator have been determined, the mechanical efficiency of the engine 
can be calculated. 

Engines of the directly-loaded class generally have the working 
machine so closely incorporated with them that the friction of the 
whole combination is the quantity in which we are interested. In the 
locomotive, tractive friction, due to the weight load on all the axle 
bearings and augmented by the rolling resistance of the wheels, is not 
separable from the friction of the engine proper: the useful output is 
determined by means of a traction dynamometer, which in a laboratory 
can be placed right behind the locomotive, but on the road must be 
between the " tender " and the train. With pumps, air compressors, 
and the like, indicators on the water or air cylinders give the readiest 
means of measuring the work output — see also § 26 (j) as to the cal- 
culation of duty. 

(6) Friction Load and Power. — If indicator diagrams be taken 
from an engine which is running light, or without external load, their 
mean effective pressure represents a driving effect just sufficient to 
overcome the friction of the machine; and from it may be calculated 
the friction horse-power. A question at once arises as to how this 
no-load friction compares with the difference between indicated and 
net power under working conditions. As an observed fact, there is 
commonly little increase of internal resistance with load. Rationally, 
the relation between friction m.e.p. or p f and total m.e.p. or p m depends 
upon the kind of friction in the machine. With very slight lubrication, 
the resistance to motion is almost proportional to the force which presses 
the rubbing surfaces together, or the coefficient of friction is nearly a 
constant. With complete lubrication, the surfaces are kept apart by a film 
of oil, and the resistance to relative motion acts within this fluid: the size 
of a bearing and the " strength " or required " body " of the lubricant 
having been determined by the heaviest force to be carried, the " friction " 
of the joint decreases very little as the external load force is removed. 

In an engine, the friction work of the piston and valves and of their 
rods is likely to increase slowly with the m.e.p.; but the mechanism 



§ 28 (&)] 



FRICTION AND MACHINE EFFICIENCY. 



277 



friction will be very much of the second type just described. With 
well-balanced valves and flooded lubrication, the friction pressure pi 
will be almost independent of p m ; with high unit pressure in the bear- 
ings and with a scanty supply of oil, pi will increase with p m , but always 
in less than direct proportion. 

(c) Typical Relations as to friction and efficiency are illustrated in 
Fig. 143. The base is indicated power, expressed in terms of rated power 
as unity, the ordinate is effective 
power to the scale at the left, 
or efficiency to the scale at the 
right. Lines or curves like AA 
and AB show actual output; 
and when the line OM of equal 
power is drawn, the vertical in- 
tercept gives the lost work or 
friction horse-power. With AA 
this difference is constant, with 
AB it increases at a moderate 
rate. The efficiency, got by di- 
viding the ordinate of the load 
line AA or AB by that of the 
power line OM (or by the ab- 



1.0 



0.5 































/ 


M 
A 
































B 
































































































i n 
































C 
































D 








































y 






























// 
































/ 






/? 


; 


















U.O 










/ 






















































ll 1 


































/ 

































0.5 



.HP. 



1.0 



Fig. 143. — Efficiency Diagram. 



scissa), is shown in the curves AC and AD for the respective cases. 
This ratio increases very rapidly with small loads, then more slowly; 
and with heavy loads the curve tends to become horizontal. 




Fig. 144. — Machine Efficiency of Sibley College Engine: see reference under Fig. 
95. Whole engine rated 150 h.p. at about 90 r.p.m. Output measured by 
brakes. 

(d) Examples of Performance. — In Fig. 144 the scheme of Fig. 
143 is modified so as to give a more compact diagram. The first ordi- 
nate AF is friction horse-power, which is laid off directly from the base 



278 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



line, instead of being an intercept between inclined lines: it is nearly 
constant for each condition of working, but develops a tendency to 
increase with the load as the engine is made more complex. The effi- 
ciency, AE, is laid out exactly as in Fig. 143. 

This laboratory engine is separable into three units, which can be 
run independently or combined as desired. From simple to compound 
there is just a little more than a doubling of the friction load, which 
seems reasonable; but when the three sections are joined together the 
lost work increases abnormally. The special reason for this does not 
appear, but the example must be taken as an extreme, not a typical, 
case of the effect of greater complexity. 

The machine efficiency of stationary engines in proper condition 
ranges from 0.80 to 0.95, with 0.90 as a good value to assume in making 
approximate estimates. 

(e) Combined Efficiency. — Some examples of the combined 
working of engines and generators are given in Fig. 145. For com- 



I.U 




t" 




Fhh 


o ■ 


T 




0.8 


o 


D 


0^ 


0.6 


A 




4 

2 




o 


p — o- 




o 


-— — ~B~ 


A- r""r"°° 




+ 


+ ^ + + 


o +■ ■ 


+M 







1 1 1 1 1 1 1 



10 



M.E.P. 20 



30 



Fig. 145. — Combined Mechanical and Electrical Efficiency, tests reported by L. S. 
Marks, reference under Fig. 97. Power quantities represented by mean effec- 
tive pressures. Principal group (circled points) from engine B, other points 
from engines C, D, E, and F. 

paring machines of differing size and speed, m.e.p. is a better quantity 
to use than horse-power. The base is m.e.p. referred to the low-pressure 
piston, and the ordinate p f represents all the losses of power from 
pistons to generator terminals. At M is given, for engine B, the mean 
pressure for friction alone, got by indicating the engine when running 
light. This may be a little low for full-load conditions, and the machine 
efficiency at N correspondingly high; but the increase of total p f with 
load, shown by the rise of the line AB, is principally due to the genera- 
tor, since the electrical losses have a decided and definite law of in- 
crease with output. 



§ 28 (c)] 



FRICTION AND MACHINE EFFICIENCY. 



279 



Generator efficiencies commonly range from CT90 to 0.97 for good 
machines at rated load, tending to rise with the size of the unit. Using 
the higher part of the range of mechanical efficiency, say from 0.85 to 
0.95, we get 0.80 and 0.92 as the limits between which the combined 
value is likely to lie — the total efficiency being, of course, the product 
of the partial efficiencies. 

This factor must be taken into account when comparing steam-rate 

performances per indicated horse-power-hour and per kilowatt-hour, or 

iS h with £ k as defined in § 26 (a). For equal powers the ratio is 0.746, 

so that 

S h + 0.746 = S k and S k X 0.746 = S h . . . . (141) 

But with a combined efficiency of 0.80 to 0.92, the electrical output 
from one indicated horse-power will be only 0.60 to 0.68 kilowatt; and 
this modified ratio will hold between steam per hour per i.h.p. and per 
kw. A good average value to remember, for use in the transformation 
represented by Eq. (141), is 0.65 in place of 0.746. 



1.0 

Eff: 

0.8 
0.6 
20 

Pf 

10 



oN0.2 22X28 

+ N0. 1. 21 X 30 

+ 



■T~ + 



40 



m 



60 M.E.P. 80 



100 



120 



140 



Fig. 146. — Results from Simple Locomotives, Pennsylvania Railroad tests as 
listed under Fig. 103; steam diagrams from No. 2 are given in Figs. 132 and 133. 
Base is total m.e.p., ordinate pi or friction m.e.p. 

(/) Results from Locomotives. — The tests represented in Figs. 
146 and 147 were made with the locomotives mounted in the usual 
laboratory fashion, on supporting wheels (one to each driver) which 
were coupled to friction brakes of the Alden type. The net work is 
calculated from the pull registered by a traction dynamometer at- 
tached directly to the locomotive proper, so that only the friction of 
the extra axle bearings is included with what strictly belongs to the 
engine. The scattering of the points is in some degree due to differ- 
ences in speed, which are not shown in the plots. Mostly, however, it 
is simply erratic, with the probable error about equally assignable to 



280 



PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 



the indicators and to the dynamometer. The exhibit is summed up 
by naming 0.85 as the average efficiency. 

In general, a machine will show less friction at fair speed than at 
very low speed, chiefly because the bearings run warmer and the lubri- 
cant is more fluid; but with very high speeds the friction becomes 
greater, because of incipient or partial failure of lubrication. 



1.0 
Eff. 

0.8 

0.6 

20 

10 



-°u~ 



I. 



oNO.3. 23.35X32 
+N0.6. 1^,25X26 



°8 



+ 
+ ++ 



&) 



40 



60 M.E.R 80 20 P. 



+ + + 


o 


o 


+ u 


+ 


o 




+ 







- 


II 


oNo.5 
+N0.7. 


14.2.23.7X25.2 
14.2.22.1X23.6 


- 






o 


o 
_o 

6 


— r 


+ 

■J-o 

r~ 


+ + o ° 

+ ♦ * 

• 1 1 



40 



60 



Fig. 147. — Results from Compound Locomotives, same source as Fig. 146. Steam 
diagrams from Nos. 3 and 5 given in Fig. 134. Base is m.e.p. referred to low- 
pressure piston. 

(g) Frictional M.E.P. — The mean frictional or waste-work pres- 
sure Pi has quite a range of variation in the various classes of engines. 
As a minimum, take from the pumping-engine tests listed in § 27 (c) 
and in Table 13 the average values E m = 0.94, p m = 24, the latter the 
m.e.p. referred to the low-pressure piston: under these conditions the 
lost work would be done by p f = 0.06 X 24 = 1.44 lb. With a rated 
m.e.p. of 40 lb. and with E m = 0.85, the value of pi will be 6.8 lb. For 
stationary engines the common range is perhaps 2 to 5 lb. per sq. in. of 
the low-pressure piston. For locomotives, with high working m.e.p. 's, 
the diagrams just given show a common range of 5 to 10 lb. and extreme 
cases of as much as 20 lb. 

This matter has a direct bearing upon the question of the proper 
degree of expansion, or "of the terminal pressure in the engine, as set 
forth in § 15 (g). 

Qi) Friction by Force Analysis. — It is obvious that if the vari- 
ant or average pressure between bearing surfaces has been determined 
by the methods of the next chapter (§ 34) and if the coefficient of fric- 
tion is known, the work against friction can be calculated in detail and 
summed up for the whole machine. This is the logical procedure from 
the side of machine design, but its quantitative validity is greatly 
impaired by uncertainty as to the coefficient of friction. For journals 



§ 28 (h)] FRICTION AND MACHINE EFFICIENCY. 281 

and bearings the latter is likely to range from 0.02 to 0.06, for the cross- 
head slide 0.06 to 0.08 is a fair assumption. The internal friction, of 
piston and valve, is even less determinable. In view of these difficul- 
ties, anything more than this suggestion of the analytical method would 
be out of place here. 

§ 29. Proportioning Engine Cylinders 

(a) Relations Involved. — The problem of determining the size 
of engine cylinder needed for the development of a certain power is 
closely related to the calculation of indicated horse-power, as set forth 
in the first part of § 21. The method is to use Eq. (115), with horse- 
power H and mean effective pressure p m as fixed quantities, and choose 
suitable values of diameter D (or area A), stroke S, and speed N: evi- 
dently, the solution is indeterminate, and there is call for an exercise of 
judgment, guided by a knowledge of practice. For a multiple-expan- 
sion engine, the size of the low-pressure cylinder will first be found in 
this manner, using the reduced or referred m.e.p., of which typical 
values are given on page C of Table 13 : the proportioning of the higher 
cylinders is another problem. 

As a prerequisite to this first step in the design of an engine, the 
mean effective pressure must be assumed or estimated. Following 
lines of thermodynamic reasoning, as summed up in § 26 (c) , .we might 
get the output W per pound of steam by applying an assumed relative 
efficiency E-& to the ideal output "FFr; then choosing a terminal specific 
volume, such as appears in all the steam diagrams of §§ 22 and 27, we 
could easily get the m.e.p. by the general method of Eq. (20), page 43. 
It is better, however, to work from the mechanical side of the subject, 
calculating the m.e.p. of an "ideal steam diagram" with the expansion 
curve pv = C, like Fig. 57, by the method of § 15 (i), then adjusting 
this by means of an empirical "diagram factor" which takes account of 
the actual losses of work area. 

(6) Ideal Diagram and Diagram Factor. — In Fig. 148 the aver- 
age combined diagram from Fig. 78 — corresponding to Fig. 82, but 
first laid out, in full line, on the ordinary plan of bringing the clearance 
lines to the axis of zero volume — is used to illustrate this matter. The 
top line AB shows steam-pipe pressure pi, the bottom line RD con- 
denser pressure p ; and the hyperbola BC is drawn through high- 
pressure cut-off, v/ith O as origin. One scheme, hich has been quite a 
good deal used, is to compare the sum of the actual work areas with 
the full area ABCDR: in this particular example, the ratio is 0.55. 

Thus to include the clearance and compression areas within the 



282 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

ideal area hardly seems desirable. The opposite extreme would be to 
use the dotted diagrams, with their compression curves brought to the 
axis OA, as in Fig. 82 and Fig. 75: then the " ideal" expansion curve 
would be HN, and AHNPR the basal area. This comparison gives a 




°9 P LG 

Fig. 148. — To Illustrate the Diagram Factor. 



high factor, here 0.84: but beside the extra graphical work involved, it 
has the great disadvantage that the base-length RP no longer repre- 
sents the cylinder volume, and hence is not a proper divisor by which 
to get m.e.p. from area. 

A glance at the examples in Table 14 will show that the degree of 
conformity to such a standard as the ideal steam diagram is low and 
exceedingly variable. Since the purpose of recorded diagram factors 
from working engines is merely to serve as a help in making approxi- 
mate estimates of probable action, simplicity and convenience are of 
more importance than logical correctness. Disregarding then the 
clearances, a simple expedient is to back the end lines of the cylinder 
diagrams up against the vertical axis. In Fig. 148 r imagine the low- 
pressure diagram to be shifted to the left until it touches the line QE, 
or lay off its length in SG, and draw the hyperbola B'F with Q as origin. 
The factor is now the ratio of the card areas to EB'FGS, and as worked 
out in Example 32, it is 0.76 for this figure. 

In the Code of Rules for Engine Tests of the American Society of 
Mechanical Engineers, Vol. 24, page 751, the method recommended is 
the one just described, except that the initial volume, measured off 



§ 29 (&)] PROPORTIONING ENGINE CYLINDERS. 283 

from E to B', is the intercept between the compression and expansion 
curves when produced up to the steam-pressure line AB, corresponding 
with GH in Fig. 107. The gain from this slight added complexity is 
questionable. 

Example 32. — In the engine and test of Figs. 78 to 82, and of Example 26, 
page 164, the data for the calculation of ideal m.e.p. and of the diagram factor 
are as follows: 

Steam pressure p x = 111, condenser pressure p = 3.9, cut-off pressure 
p = 90, all in pounds absolute; mean high-pressure cut-off at 0.295 of the stroke, 
and cylinder ratio equal to 2.36; m.e.p. referred to large piston, p m «= 25.0 lb. 

Taking the nominal high-pressure volume as unity, the expansion ratio 
from initial cut-off to terminal volume, or from v x = 0.295 to v 2 = 2.36 is 
2.36 ■*■ 0.295 = 8.0; while the total ratio, from p x = 111 instead of from p = 90 is 

r = 8.0 X ^ = 9.87. 

Substituting this in Eq. (102), we get the ideal m.e.p. ' 

1 + log e r 111w 3.289 „ n 

Pmi = Pi r Se " Po = HI X -^r - 3.9 

= 37.0 - 3.9 = 33.1. 
Then the diagram factor / is 25.0 4- 33.1 = 0.756. 

(c) Examples of the Diagram Factor. — Data and results from 
nearly all the steam diagrams in this Chapter, with a few from simple- 
engine diagrams in Chapter V, are collected in Table 14. The factor 
/, in the last column, varies widely. The tests may be briefly discussed 
as follows: 

Numbers 1 to 6 are large-compression engines, and have big kinetic 
losses — compare § 19 (j). In the locomotives, Nos. 2, 3, and 4, the 
latter include the effect of the high back-pressure caused by the exhaust 
nozzle. The very low values, 3b and 4b, are due to excessive com- 
pression. Typical ranges of / in this class are, for simple engines, 0.80 
to 0.85, for multiple-expansion engines, 0.70 to 0.75. 

The remaining tests are from engines of the small-compression class, 
No. 7 simple, 8 to 10 Corliss or equivalent compound, 11 to 14 pumping 
engines. The normal range of / seems to be from 0.85 to 0.95. In 
Nos. 9 and 12, the high factor results from strong jacket action, which 
holds up the value of pv (relative to that at high-pressure cut-off) as the 
steam expands. In engine 10, the low factor is due to large kinetic 
losses, together with a very considerable compression effect — see 
Fig. 137: but in spite of this, the engine has a very high relative 
efficiency. 



284 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

That / exceeds unity in test 7b is due to the assumptions upon which 
p m i is based. Omission of the clearance volume makes the curve like 
B'F in Fig. 148 drop so rapidly that on a diagram such as No. 15 of 
Fig. 90 it will fall below the actual expansion curve. Commonly, this 
diminution of the ideal area and mean pressure is decidedly over- 
balanced by the decrease of actual area through compression; but here 
the compression is very small and the factor comes out too big. 

The amount of empirical knowledge really needed for an intelligent 
choice of the diagram factor to be used in any case is enough to guide 
the more definite operation of blocking out the steam diagram and 
sketching in curves which are likely to be quite nearly realized in the 
engine. 

From a glance down the p m column of Table 13, it appears that the 
m.e.p. for rated load, referred to the low-pressure piston, ranges from 
about 25 in stationary engines of the more economical types to 40 in 
those engines which are required to give a larger output of power per 
unit of space and weight. 

(d) Determining Size and Speed. — Having i.h.p. H and m.e.p 
p m , and putting the factor 2 into Eq. (115) for a double-acting engine, 
we get the equation of relation 

ASN = 198,000—, 

Pm 

or Z) 2 £2V = 252,100 — (142) 

Pm 

This can be made determinate by fixing N and choosing a ratio be- 
tween D and S, or by assuming a value of the piston speed 2 SN/12. 
The method of handling the problem of size and speed will best be 
shown by a couple of examples. 

Example 33. — Find suitable cylinder dimensions for a high-speed engine, 
like that in Fig. 2, which is to develop 110 i.h.p. on 36 lb. of m.e.p. 

In this type of engine, the diameter and stroke are nearly equal. First 
lettering S = D and substituting in Eq. (142) we have, 

™ = 252,100 X 110 = 770,300 
N X 36 N 

Make several solutions with different speeds: 

N = 200 225 250 

D z = 3852 3424 3081 

D =S = 15.68 15.07 14.55 






§ 29 (c)] PROPORTIONING ENGINE CYLINDERS. 285 

Table 14. Examples of the Diagram Factor. 



No. 


Fig. 


Condition. 


Pi 


Po 


V 

90 


e 


R 


r 


Pmi 


Pm 


/ 


1 


84 


1-14-15-225 


120 


14.7 


.333 




4.0 


57.0 


48.0 


0.84 


2a 


133-5 


1-21-30-80 


218 


14.4 


190 


.171 




7.1 


77 


64 


0.83 


b 


8 


■80 


219 


14.4 


179 


.410 




3.0 


139 


117 


0.84 


3a 


134 1 A 


2-35-32-80 


221 


14.4 


160 


.610 


2.34 


5.3 


102.3 


74.8 


0.73 


b 


B 


160 


223 


14.4 


160 


.431 


2.34 


7.6 


74.5 


35.8 


0.48 


4a 


134 II A 


2-24-25-160 


223 


14.4 


160 


.568 


2.81 


6.9 


80.0 


53.3 


0.67 


b 


B 


240 


234 


14.4 


160 


.322 


2.81 


11.6 


52.0 


30.5 


0.58 


5 


135 1 


3-70-48-72 


153 


2.7 


110 


.663 


5.70 


12.0 


41.7 


30.5 


0.73 


6 


135 II 


3-57-39-61 


170 


0.7 


110 


.455 


6.75 


22.9 


29.8 


21.4 


0.72 


7a 


90-1 


1-17-30-70 


104 


14.4 


80 


.687 




1.9 


76.0 


64.0 


0.84 


b 


15 


86 


106 


14.4 


80 


.140 




9.5 


22.0 


26.0 


1.18 


8 


136 A 


2-56-72-65 


138 


2.1 


110 


.311 


3.48 


14.1 


33.7 


27.6 


0.82 


9 


136 B 


2-34-60-34 


149 


0.5 


130 


.199 


4.18 


24.1 


24.4 


23.4 


0.96 


10a 


137 A 


2-86-60-75 


190 


1.0 


160 


.23 


4.30 


22.2 


34.1 


26.0 


0.76 


b 


B 


75 


199 


16.1 


160 


.40 


4.30 


13.4 


37.4 


26.4 


0.71 


c 


C 


75 


195 


12.1 


160 


.53 


4.30 


10.1 


51.9 


38.6 


0.75 


11 


129 


2-42-36-20 


97 


2.0 


84 


.468 


4.04 


10.0 


30.0 


26.8 


0.89 


12 


130 


2-54-120-19 


157 


1.0 


130 


.202 


4.02 


23.2 


26.3 


25.0 


0.95 


13 


1311 


3-74-60-20 


136 


1.2 


130 


.363 


7.11 


20.5 


25.5 


22.1 


0.87 


14 


131 II 


3-80-60-21 


169 


1.6 


150 


.366 


7.66 


23.6 


28.2 


24.0 


0.85 



For fuller information about the engines, see the figures referred to. 

Under Condition, the first number shows the stages in expansion (1 = simple, 
2 = compound, 3 = triple expansion), the second the diameter of the low-pressure 
piston, the third the stroke, the fourth the speed in r.p.m. 

The other symbols are all defined in Example 32, which illustrates the method of 
calculating expansion ratio r, ideal mean pressure pmi, and diagram factor /. Pres- 
sures pi, p , and p m , also cylinder ratio R, have the same meaning as in Table 13, 
where most of these tests appear; but cut-off e is different, corresponding with 
RB/MN in Fig. 73, while p is the same as OS in that figure. 

The determinations for the above table are all made from the diagrams as redrawn 
for this book; further, in most cases, the conditions belonging to a particular set of 
indicator cards are not the same as the average conditions for a long test: these 
reasons account for the small departures from Table 13 which will be noted on close 
comparison. 



Using simple dimensions in 


inches, 






Let D = 15.5 


15 


15 


14.5 


and S = 16 


15 


14 


15 


then SD 2 = 3842 


3375 


3150 


3154 


and N = 200.3 


228.2 


244.4 


244.1 



Which of these solutions to use is a matter of choice. 

Example 34. — Find the diameter of the low-pressure cylinder of a com- 
pound engine which will develop 2000 i.h.p. on 25 lb. of referred m.e.p., with a 
stroke of 60 in. and at a speed of 75 r.p.m. 



286 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

By Eq. (142), 



and 



a = 252,100 X 2000 = 

60 X 75 X 25 
D = 66.95 or 67 in. 



If the piston speed had been given as 750 ft. per min., the values of S and 
N would have been open to choice. 



AmB 



AhB' 




Fig. 149. — A Three-stage Diagram 
with Complete Expansion. 



Fig. 150. — The Introduction of Terminal 
Drop. 



(e) The Pkoblem of Cylinder Ratio. — In dividing the total oper- 
ation among the two or more stages of a multiple-expansion engine, a 
fairly equal distribution of work among the pistons and the avoidance 
of excessive loss by incomplete expansion in the higher cylinders, or 
through receiver drop, are the important objects to be kept in mind. 
The showing of Fig. 76, where with equal work division there is very 
nearly the same temperature range in both stages, is so closely typical 
that, as a general thing, the question of temperature range may be left 
to take care of itself. 

Retaining the ideal conditions of Fig. 76, including a constant re- 
ceiver pressure, and adding the requirement of complete expansion in 
all stages, consider the problem of dividing area ABCD, Fig. 149, into 
three equal parts. With the expansion curve pv = C, and using com- 
ponent areas as in § 15 (i), we have 



area ABEF orii = piVi ( 1 + log e - J — P2V2 

= pv loge n, 



(143) 



§ 29 (e)] 



PROPORTIONING ENGINE CYLINDERS. 



287 



letting pv stand as a general value for the curve BC. Similarly, 
FEGH = A 2 = pv log e r 2 ; HGCD = A 3 = pv log e r 3 . 

For equal partial areas Ai, A 2 , and A3, the individual expansion 
ratios must be equal, or 

v 2 Vz v 4 

- = - = — = r; 

Vi v 2 v 3 

further, the -total ratio R or v 4 /vi will evidently be the product of r h r 2 , 
and r 3 : wherefore, in this case, R = r 3 ; or in general, for n stages, 

R = r n (144) 

Note that here, as compared with Art. (6), it has been convenient to 
assign new meanings to r and R. 

In Fig. 150 the expansions are cut short at the volumes indicated by 
dotted lines in Fig. 149; and to equalize areas the cut-offs are moved up 
a little in stages 2 and 3, raising the receiver pressures above the orig- 
inal levels which are dotted in on Fig. 150. Usually, the amount cut 
away from the last stage is relatively much greater than from the earlier 
stages. 

(/) Equalization of Work Areas. — Coming back to the com- 
pound engine, as in Fig. 76 and in Fig. 151, and using subscripts cor- 



a Bi B 2 B 3 B 4 p 




Fig. 151. — Diagrams Showing Equal Division of Work, with variation in the cut- 
off in both cylinders. 

responding with the numbers 1, 2, 3, 4, and on both diagrams, we 
have the fundamental relation, 

P1V1 = P2V 2 = pzv z = P4V4 (145) 



288 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

The areas are, 

ABCHJ = Ai = pi; (l + log e ~) - p*v 2 ; . . . (146) 

JDEFG=A2=2w(l+log e ^-p^4. . . . (147) 

Equating and dividing by pv, using the particular values in Eq. (145) 
as convenient, we get 

i v 2 v 2 , v 4 Po /1/1oN 

log %-I - £ = Iog ^ - p t (148) 

If there is to be no receiver drop, or if v s = v 2 , and if further we let 
v i = Ev4, this becomes 

SG Evi se v 2 pi 

* e E\vJ pS 

V f=^E y anti-log (l-^) = CVE. . . . (149) 

This E, which may well be called the ratio of total cut-off, is the recip- 
rocal of R above; the cylinder ratio v±/v 2 is no longer the square root 
of R, but it is proportional to that root according to a factor which 
depends upon the ratio of final pressure-drop, po/p*. 

Equation (149) is the only application of Eq. (145) that is of real, 
practical use. It is to be considered as fixing, not the high-pressure 
cylinder volume v 2 , but rather the low-pressure cut-off volume Vs, and 
with it the receiver pressure. Having thus gotten an approximate value 
for p 3 , the best procedure is to draw the line JD tentatively, choose a 
v 2 which gives a reasonable receiver drop, then lower JD, by trial and 
planimeter measurement, until equality is reestablished. 

(g) Variation of Load. — In Figs. 151 and 152, the heavy-line dia- 
grams marked by the subscript 2 are supposed to represent the best 
working of the engine, at its proper, rated load. In Fig. 151, the 
division of work is kept equal as the power of the engine — determined 
chiefly by high-pressure cut-off — varies over a wide range. To secure 
equality, the low-pressure cut-off must also change: here D has a wider 
range on the base MN than B has on MQ, and D is always later in the 
stroke than B. In this diagram we see that at big loads there is an 
excessive receiver drop, while in case 1 the expansion curve BiCi sinks 
below the exhaust line JiHi, forming a negative-work loop just as in a 
simple engine under similar conditions, and with a corresponding loss 
of efficiency, according to the reasoning of § 15 (gr). In the whole action, 
the receiver pressure varies over a comparatively narrow range. 



§ 29 (g)] 



PROPORTIONING ENGINE CYLINDERS. 



289 



Fig. 152 shows the other type of relative valve action, the low- 
pressure cut-off remaining fixed while the high-pressure cut-off changes. 
The result is a wide variation in receiver pressure, and a decided depar- 
ture from equality in work division; but the receiver-drop loss is kept 
down to a very moderate amount with any load. 




M Q N 

Fig. 152. — Constant Cut-off in the Low-pressure Cylinder. 

(h) General Relations. — The showing of Arts, (e) to (g) will 
now be briefly summed up, for the two-stage engine, with the addition 
of a few almost self-evident conclusions as to the result of certain other 
variations in condition. For the cycle of any engine, the fundamental 
determinants are initial pressure pi and exhaust pressure p ; and the 
primary variable with load is the first or high-pressure cut-off, upon 
which directly depend the total expansion ratio R = v±/vi and the ter- 
minal pressure p±. 

With these leading dimensions of the cycle fixed for a compound 
engine, the division of work between the cylinders depends chiefly upon 
the receiver pressure, and this in turn upon the low-pressure cut-off. 
As the latter is earlier, it raises the admission pressure in its own 
cylinder, increasing mean effective pressure and share of work; the 
effect is just the opposite of that produced by a change in the initial 
cut-off which determines amount of steam admitted. 

With the load constant, the work done in the high-pressure cylinder 
is increased, 

(a) By making the low-pressure cut-off later. 

(6) By raising the boiler pressure : this slowly diminishes the prod- 
uct pv, or the amount of steam admitted to perform a given amount 



290 PERFORMANCE AND EFFICIENCY OF ENGINES. [Chap. VI. 

of total work per revolution; and with a fixed low-pressure cut-off vol- 
ume vzi the receiver pressure p 3 is lowered. The addition to the high- 
pressure diagram because of a higher admission line and a lower exhaust 
line is greater than the loss from moving the expansion curve inward. 

(c) By raising the exhaust pressure of the engine: this subtracts 
more from the bottom of the low-pressure diagram than is added on 
account of the increase in pv and the consequent rise in receiver pressure. 

With variable load and a fixed low-pressure cut-off, the high cylinder 
takes a larger share of a small load, a smaller share of a large load, as 
appears from Fig. 152. For equality, the two cut-offs must vary to- 
gether, but not in exactly the same manner. 

• (i) Cylinder Proportions. — The influences taken into account 
in Art. (e) do not fix the cylinder ratio with any exactness, so that there 
is always a considerable element of judgment in the design of multiple- 
expansion engines. In Fig. 76, for instance, it is evident that v% can 
be varied over quite a little range without much change in total work 
or in work division, only the receiver drop showing a large relative 
variation. The general idea of Eq. (444) -underlies the whole matter, 
but that simple progression is only very roughly followed. 

In summary and extension of the information in the R column of 
Table 13, it may be stated that in practice the overall volume ratio 
ranges from 2 to 5 in compound and from 5 to 10 in triple and quadruple 
engines, with 2.5 to 4 and 6.5 to 9 as the regions within which most 
engines are found. The smallest ratios are used in compounds which 
need a big high-pressure cylinder for the sake of liveliness in reversing, 
as in mine hoists and reversing rolling mills. Large-compression en- 
gines have smaller ratios between the cylinders than have those with 
small compression and fuller expansion in the individual stage. The 
high-ratio compound, represented by tests 28 and 29 in Table 13, is a 
special type in which the aim is to get very long expansion with but 
two cylinders: as against the triple arrangement, it saves the kinetic 
losses of one transfer of steam, but to balance this it has relatively 
more receiver drop, and perhaps a little bigger cylinder loss. 

Limitation of space forbids further exposition of this subject here: a 
large number of examples, in tabulated form, will be found in Steam 
Engine, Vol. II, pages 506 to 509. 



CHAPTER VII 
WORKING AND CONSTRUCTION OF THE ENGINE 

§ 30. Forces in the Machine 

(a) In This Chapter will be considered the force actions within the 
reciprocating engine and the motions of its parts, and typical examples 
will be given of the construction of the members of the main engine 
mechanism. The discussion of force action begins with steam pressure 
on the piston and runs through to the final working force, which meets 
and overcomes the load resistance. In the study of motion, the de- 
termining fact is that, through the influence of the fly wheel, the crank 
shaft is constrained to practically uniform rotation; therefore we reason 
from the shaft back to the piston. 

The total or mean effect of the steam pressure, in doing work upon 
the piston, has been fully considered in § 21 (6) to (d) : further develop- 
ment along that line has been carried out in §§ 28 and 29. The instan- 
taneous, variable force action in the engine is the principal subject now 
before us, and the first step is to take a general view of the whole sys- 
tem of working forces. In this, and in the more detailed discussion of 
later sections, friction is not taken into account, or ideal mechanical 
working is assumed. Further, the force of gravity on the reciprocat- 
ing parts is practically omitted: in a horizontal engine its effect in the 
direction of the main force action is insignificant; in a vertical engine 
it can be very simply included, in a manner which is noted in § 32 (c). 

In Fig. 153 all the forces that have to do with work performance 
are represented graphically, upon an outline of the engine, showing 
instantaneous conditions for a particular position of the mechanism. 

(6) Forces on the Piston Slide. — Upon the sliding piece made 
up of piston, piston rod, and crosshead act forces shown first on the 
main figure, and then, in combination, at A. These are: 
Pf — forward steam pressure, the full, absolute pressure acting on the 

forward-moving or driving side of the piston at the instant. 
Pjb = back pressure, on the exhaust or return-stroke side of the piston. 

291 



292 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



Then 

Pe = Pf — Pb is the effective steam pressure on the piston. 

F x — inertia force of slide, its reaction against the acceleration essen- 
tial to its rapidly changing velocity. 

Pd = Pe~ Fx is then the final effective driving force, delivered at the 
wrist pin W for transmission to the crank. 



Pf 



|^/^^^^^ 



g 



K P B 







Fig. 153. — Forces on the Moving Parts. 

These forces may be expressed either in pounds per square inch or 
as total forces on the piston, bringing in the area factor A, according to 
the relation P = p X A. The steam pressures are usually got from 
indicator diagrams, and it is then more convenient to keep them in 
pounds per square inch and bring the other forces to the same terms. 
Here, however, we are considering total effects; so that what are really 
distributed forces, spread out over the surface of the piston or the mass 
of the slide, are reduced to and represented by single, concentrated 
forces along the axis. 

From the beginning to, approximately, the middle of the stroke, the 
slide is being accelerated, and the inertia Fx points in the direction 
shown, against the forward driving force; but in the second half of the 
stroke the slide is retarded (or its acceleration is negative), and Fx then 
reverses. At high speeds, this force due to the mass and motion of the 
working parts modifies very materially the play of the resultant steam 
pressure Pe- 

Considering just the one position shown, the work being done upon 
the piston by Pe is not all transmitted to the crank, but part of it is 
being stored in the slide as kinetic energy. Since, however, the slide 
has zero velocity at each end of the stroke, the inflow and outflow of 
energy must balance; and, as a net result, all the effective steam work 
will be carried over to the crank. 



§ 30 (c)] FORCES IN THE MACHINE. 293 

(c) Transmission to the Crank. — The principal forces in equilib- 
rium at the wrist pin are Pd and Pw, the latter the pressure of the con- 
necting rod upon the pin; but since these are, in general, not in line, the 
third force essential to equilibrium is supplied by the guide reaction 
Qg, perpendicular to the slide bar. In this figure, Q is used to indicate 
a force which does not move in the direction of its action — that is, 
one which acts upon a body that does not thus move — so that it can- 
not do work. A simple trial of conditions during the return stroke 
(see Fig. 162) will show that with both the rod slant and the force Pd 
reversed, Qg will act in the same direction as during the forward stroke. 

The connecting rod WC has, of course, an inertia force of its own, 
which would have to be determined and taken into account in order to 
find the exact manner of the force transmission. This is a difficult opera- 
tion, and it is usual to adopt the approximation of considering a part 
of the mass of the rod concentrated at W, where it adds itself to the 
slide and increases F h and the rest at C, where it has a radial, cen- 
trifugal inertia force, with no turning effect upon the crank. Then the 
rod can be taken as a weightless link, transmitting force along the 
center-line from W to C. 

Coming now to the crank pin, we have the force Pc, equal to Pw 
reversed, exerted upon it by the connecting rod. Resolving this into 
components perpendicular to and along the crank arm OC, T is the 
turning force, or force tangential to the crank circle, while Qn is the 
radial component, which simply presses the shaft against the bearings. 

This turning force T, with the lever arm R, must equal in effect the 
resistance T\, here taken tangential to the wheel, at the radius Pi. 
In the aggregate the average moment TR must equal TiRi; but since 
T varies widely, equilibrium exists only at certain positions of the 
engine: in all others there is an unbalanced turning moment, free to 
give angular acceleration to the shaft, and acting against the moment 
of inertia of the fly wheel, represented by the couple Pw-Pw- 

Under the assumption that no work is lost through friction, the 
work done by T upon the crank in one revolution must be the same as 
that done upon the piston by the steam pressure. During each stroke 
the piston moves through the distance 2 R, the crank pin through irR; 
using the subscript m to mark mean values, we have 

P E m X 2P = P Dm X2R = T m XirR; 

whence, using P m for either m.e.p., 

T m = -P m = 0.6366 P m (150) 

7T 



294 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

(d) Exact Force Action on the Connecting Rod. — This is 
illustrated in Fig. 154, the explanation of which is as follows: 



$ 




% 


K 






~~~i£ 


0^2 






Fig. 154 




Forces 


on 


the Connecting Rod. 



Assuming the total inertia force F 2 — the concentrated resultant of 
the small inertias of the distributed particles of the rod — to be known, 
we may replace it by parallel components at the pins Pw at W, Fc at C. 
Now besides transmitting force along its center-line, the rod must re- 
ceive from the pins component forces equal and opposite to Pw and Fc, 
respectively. Or, conversely, the pressure Pw on the wrist pin will be 
the resultant of Ps, along the rod, and Pw By a method the develop- 
ment of which belongs to the graphics of machine forces, it is possible 
to make the resultant of Pd and Qq equal that of Pw and Ps : and then 
carrying this Ps over to C and combining it with Fc, we get the other 
pin pressure. 

For the sake of knowing how nearly correct is the approximation to 
rod inertia described in Art. (c), the inertia effect of the rod was fully 
worked out, for a typical case, in The Steam Engine, Vol. I, §§ 37 and 
38. It was there established that the scheme of "concentrating" the 
rod mass in two parts at the pins is amply accurate for all practical 
purposes. The exact discussion is not reproduced here, for it really 
belongs to the subject of mechanics of machinery rather than to a 
study of the steam engine. 

(e) Equilibrium op the Shaft. — In Fig. 153 the system of forces 
acting on the shaft is not complete, because the pressure with which 
the bearings balance the resultant of all the other forces is not included. 
The complete set of forces is shown in Fig. 155, several being added to 
those given on Fig. 153. An important mechanical principle which 
applies in this case is shown at II, and may be stated as follows : 

If the force P acting upon a body does not pass through the center 
or axis about which the body is compelled to turn, this force will 
have two effects : it will tend to push the body straight ahead in its own 
direction, as though a force Pi equal and parallel to itself were applied 
at the center, and resisted by the equal and opposite reaction of the 
bearing; and will also exert a turning moment, that of the couple made 
up of P and B*, tending to turn the body about O. 



§ 30 (e)J 



FORCES IN THE MACHINE. 



295 



In order, then, to find the pressure on the bearing, we have only to 
combine all the forces acting upon the shaft, whether they pass through 
the center or not. On Fig. 155 these forces are: — 




Fig. 155. — Forces on Shaft and Wheel. 

Pc = pressure of connecting rod on crank pin. 
W — weight of whole rotating piece. 

L = resultant load force : here the power is supposed to be taken from 
the engine by a belt, the difference between the two tensions, L\ 
on the tight or driving side and L 2 on the slack side, being equal to 
the T\ on Fig. 153. Then L is the resultant of the two belt pulls. 
Fb = centrifugal force of the counterweight: this is an eccentric mass, 
attached to the crank opposite the crank pin, in order that its cen- 
trifugal force may partly balance the inertia force F\ of the recipro- 
cating parts, in a manner which will be explained presently. 
The resultant of these four forces is found in the force polygon at 
III, by laying them out in order and drawing the closing side B: as 
marked here, its arrow against the others, it is the resultant; as drawn 
in I it is the equilibrant, the reaction of the bearing against the shaft. 

Of these forces, the one that shows the greatest variation in character 
is the load L. In many cases — as when the engine is direct-connected 
to an electric generator, or to a screw propeller — the resistance is a 
simple torque, with no tendency to press the shaft upon the bearing in 
any particular direction. In a locomotive, the resistance is tangential 
to the driving wheels. In direct-acting air compressors and pumps, 
where the whole engine mechanism is used merely to regulate the speed 
and stroke, no power being taken from the shaft, the only resistance to 
the turning moment on the crank is the angular inertia of the wheel, 
again a simple torque. ■ 



296 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

With the symmetrical arrangement of the center-crank engine in 
Figs. 2 and 7, it is strictly correct to consider the forces on the shaft as 
all acting in one vertical plane. But in some cases this is only a repre- 
sentation of resultant effect: with a side-crank engine, for instance, it 
is necessary to go through quite a complex analysis in order to de- 
termine the forces on the bearings and the stresses in the shaft. 

(/) The Forces on the Engine Bed, on account of steam pressure 
and of the inertia of the reciprocating parts, are shown in Fig. 156. 
The resultant of the two steam pressures on the cylinder heads is Pe. 



yspp0%00000fl^ 




mmzmzmm&w/, 



Fig. 156. — Forces on the Engine Bed. 

The driving force Pd combines with the guide reaction to give the 
crank-pin pressure Pc; and this, transferred to the center of the shaft 
according to Fig. 155 II, and there resolved back into its components, 
gives the forces Qg and Pd as exerted upon the bearing (the bed) by 
the shaft. 

Considering horizontal forces, it appears that the bearing pressure 
Pd is less than the steam reaction Pe, so that the engine bed is not in 
static equilibrium. Separating Pe into two parts, as at A, one equal 
to Pd, the other to Pi, we see that the working forces proper do form a 
balanced system within the machine, as shown by the opposing Pd's; 
but the absorption of a part of PE-on-the-piston in accelerating the 
latter, or overcoming the inertia Pi, leaves the corresponding part of 
PE-on-the-cylinder as an unbalanced force, free to accelerate the whole 
body of the engine in the other direction. A close analogy exists be- 
tween this state of affairs and the recoil action in a gun: there the 
entire working pressure of the powder gases (barring friction) acts to 
accelerate the projectile, and reacts upon the gun and its mount with 
a force exactly equal to the inertia of the projectile; similarly the en- 
gine, accelerating the slide in one direction, is pushed the other way by 
a force identical with the inertia force of the slide. This force, rapidly 
changing and reversing, tends to produce a shaking effect — which 
will be a mere tremor, perhaps imperceptible, with massive founda- 
tions, but may become a very serious vibration where the foundation 
mass is relatively small, as in marine engines especially. 

The two vertical forces, Qg at W and at 0,-Fig. 156, form a couple; 



§ 30 (/)] 



FORCES IN THE MACHINE. 



297 



and since this is the only turning moment exerted upon the bed, it 
must, on general principles, be equal to, and in a sense the reaction 
against, the moment TR produced by the steam pressure upon the 
crank. It is through this couple that the load torque is felt by the 
engine bed. 

If the load force, like L in Fig. 155, is steady and uniform, it simply 
develops a stress in the foundation bolts, which can easily be provided 
for. 

(g) Counterbalancing. — The device used to diminish the shak- 
ing effect of the inertia of the moving parts is shown in Fig. 157. This 
consists in placing an eccentric mass on the crank disc, opposite the 




Fig. 157. — Effect of the Counterbalance. 

pin: resolving its centrifugal force Fb into horizontal components H 
and V, we see that the former acts against F h reducing the free hori- 
zontal force to (Fi — H). Of course, this introduces a free, variant 
vertical force V; and the proper relative magnitude of (Fi — H) and V 
is a question to be determined by the conditions of service. The forces 
Fi and H vary in about the same manner, as the crank rotates, so that 
the ratio between them remains nearly constant; and V varies like H, 
but with a different timing of cycle. The general idea in counter- 
balancing is to go as far as possible toward producing equilibrium 
within the system of inertia forces or of moving bodies. A discussing 
of simple counterweighting (with essentially the arrangement outlined 
in Fig. 157) is of most importance for the common two-cylinder loco- 
motive, because the vertical component V enters into the pressure of 
wheel on rail, giving to this pressure a cyclical fluctuation. The more 
complex multiple-unit engines, with a number of cylinders and cranks, 
can be and generally are so arranged that the several sets of moving 
parts pretty effectively balance each other as to inertia effect, without 
the use of extra masses for counterbalance. 

(h) Order of Procedure. — We have now covered in a general 
way the whole matter of the actions of the forces in the working mechan- 
ism or "main train" of the engine. The next step is to go over the 
same ground in detail, developing methods of determining the values of 



298 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

all the forces, and studying the manner and the effects of their varia- 
tion. The steam pressure is determined (and determinable) only by 
the indicator diagram, whose form we already know: this leaves the 
inertia force as the important unknown quantity; and to find out its 
value we must make a complete study of the motion of the engine. 

§ 31. Motion of the Engine Mechanism 

(a) Constrained Motion. — In any problem upon the motion of 
freely-moving bodies, it is necessary first to know the forces acting, 
and then to determine the resulting movements. In a machine, how- 
ever, the parts can travel only in certain definite paths; and when, 
further, a major condition can be imposed which will entirely determine 
the motion of one part, those of the others may be derived by purely 
kinematic (that is, geometric) methods. In the steam engine this 
major condition is that the shaft or crank shall rotate at uniform speed. 

This uniform rotation is, of course, secured by the use of a fly 
wheel, and in no engine is the uniformity absolute. But in the vast 
majority of cases the variations in rotary speed, within the revolution, 
are insignificant, and their effect upon the very large accelerations of the 
reciprocating parts is negligible. 

(6) Harmonic Motion. — Before taking up the actual engine 
mechanism, consisting of bed, slide, connecting rod, and crank, we will 
discuss the simpler mechanism outlined in Fig. 158. Instead of the 
connecting rod, there is a cross-slot SS formed in the slide TT, in which 





Fig. 158. — The Crossed Slider Crank. Fig. 159. — Diagram of Piston 

Displacement. 

works the small block W surrounding the crank pin C. The simplest 
motion that can be gotten from, or determined by, a rotating crank is 
the harmonic motion of the projection D, of the pin center C upon the 
diameter AB, along that diameter. In the common mechanism this 
simple, symmetrical movement is modified by the effect of the angular 
swing of the connecting rod. In many approximate discussions, the 
ideal harmonic motion is used instead of the actual, because it is simpler, 



§ 31 (&)] MOTION OF THE ENGINE MECHANISM. 299 

and because it represents the average working of the engine in both 
strokes. 

Throughout the following discussions, these symbols will have in- 
variable meanings: 

R = radius of crank, or length of crank arm. 

S = length of stroke, twice R. 

L = length of connecting rod. 

a = crank angle, measured from the left-side dead-center line OA, 

in the direction of rotation. 
/3 = rod angle, between connecting rod and stroke line; see Fig. 159 

or 162. 
N = r.p.m. of shaft. 
6 = angular velocity of crank. 

s = piston travel or displacement, AD, from beginning of stroke. 
Vq = linear, tangential velocity of crank pin, taken to be constant 

in any particular case. 
v = velocity of piston (or slide) . 
a Q = acceleration of crank-pin center. 
a = acceleration of slide. 

The piston displacement is given by the diagram in Fig. 159 : it is 
measured from A, and its value is 

AD = AO - DO, or s = R(l- cos a). . . (151) 

For the return stroke, from B to A, made while the crank is passing 
through the lower half of the circle, we can get the same relations by 
estimating a from OB and s from B; but in many cases it is better to 
carry a all the way from deg. to 360 deg., keeping the same initial 
point for s. 

Now it is self-evident that if we resolve either the velocity or the 
acceleration of C into vertical and horizontal components, the first will 



22? 

R 



C -^ \ 



\ / 



^1 



\ 



AT To ^B Al ^6^ IB 

Fig. 160. — Velocity. Fig. 161. — Acceleration. 

belong to the motion of the block W in the slot, the second to the motion 
of the whole slide. Then in Fig. 160, v being laid off from C per- 
pendicular to OC, its horizontal component is 

V = Vq sin a (152) 



300 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

We know that when a point travels in a circular path with the 
velocity v , its acceleration, radially inward, is a = v 2 /R, where v is 
in feet per second and R in feet, if a is to be in feet per second per 
second, the same term as g, the acceleration of gravity. Laying off 
this a as shown in Fig. 161 and resolving, we get 

a = a cos a = -^ cos a (153) 

a 

(c) Analytical Derivation. — The same results can be obtained 
by an analytical method which will be especially useful when we come 
to the actual engine mechanism. In a very short time dt the piston 
will travel the distance ds; and, under the action of acceleration, the 
velocity will change by the amount dv: then from the primary definitions 
of velocity and acceleration, 

-ap .'•■;••• < 154 > 

a = Tt = de (155) 

Also, the relation between the linear motion of a point at the end of 
radius R and the angular motion of this radius is, 

v Q dt = Rda; 

both sides of the equation giving the distance traversed by the point 
C in the time dt; therefore 

t = °= v i ^ 

Now starting with Eq. (151), s = R (1 — cos a), we get by suc- 
cessive differentiation, 

v = -j- = R sin a -rr = v sin a, . . . . . (157) 
dt dt 



and 



d 2 s da Vq 2 /ieo\ 

a = -T-r = Vq cos a -rr = ~FT cos a (158) 

dt 2 dt R 



Example 35. — For two typical cases, first of 48 in. stroke and 80 r.p.m., 
second of 15 in. stroke and 250 r.p.m., calculate angular velocity of crank, 
linear velocity of crank pin, and centripetal acceleration of crank pin. Also, 
assuming infinite connecting rod, find velocity and acceleration of the slide 
when the crank is at 60°. 

These two engines have nearly the same piston speed (average), the num- 
bers being 625 and 640 feet per minute, respectively. 

The angular velocity is measured in radians per second, one revolution 



§ 31 (c)] 



MOTION OF THE ENGINE MECHANISM. 



301 



equaling 2 ■* or 6.2832 radians. Running parallel columns for the two cases, 
the first results are. 



Case 1. 



N 



= 2*^ = 6.2832 x 1.333 = 8.378 
oO 



Case 2. 

= 6.2832 X 4.167 = 26.180. 



Having computed, it is easiest to get the velocity, in feet per second, by 
v = Rd, with R in feet: otherwise, it is better to find circumference of crank 
circle in feet and multiply by revolutions per second. Using and reducing 
\ S to feet for R, 



y o = JL X = 2x 8.378 = 16.756 
24 



v = 0.625 X 26.180 = 16.363. 



By circumference and revolutions per second the computation is, 



v ° = 75 jL = 12 - 566 X L333 
12 60 



16.755 



v = 3.927 X 4.167 = 16.363 



For the centripetal acceleration, expressed in feet per second of velocity- 
change per second, 



_ v<? 16.756 2 
a °-~R-~~2~ 

= 150.4 



1.22417 
2.44834 
0.30103 
2.14731 



ao = 



16.363 2 



0.625 

= 428.4 



1.21386 
2.42772 
9.79588 
2.63184 



Note how much greater is the acceleration in the small " high-speed " 
engine, although both have nearly the same velocity of crank pin: the ratio of 
centrifugal force to gravity force, at the center of the crank pin, or ao -5- g, is 
about 4.7 in the larger and 13.3 in the smaller engine. 

Finally, with the crank at 60°, where sin a = 0.8660 and cos a = 0.500, 
the piston velocity and acceleration are, 



v = Vo sin a = 16.76 X 0.866 = 14.53 
a = ao cos a = 150.4 X 0.5 = 75.2 



v = 16.36 X 0.866 = 14.17 
a = 428.4 x 0.5 = 214.2 



(d) Piston Movement. — The actual engine mechanism, some- 
times called the slider-crank mechanism, is reduced to skeleton outline 



^ Forward 




Fig. 162. — The Slider-crank Mechanism. 

in Fig. 162. Crank travel is estimated from OA, all the way round the 
circle, the latter being divided into quadrants as indicated, and the 



302 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

piston movement is divided into forward and return strokes. When the 
crank is at A and the piston near the plain cylinder head, the engine is 
said to be on its head-end dead center; the other end, OB, is called the 
crank end. The whole piston slide is represented by the plain block 
atW. 

The limits of the piston stroke are determined by making 
AM = BN = L. The piston travel, as shown in Fig. 163, is not AD, 
but MW, found by striking off CW from C as a center. A construction 
which will give this travel s for any crank position, without the trouble 
of thus striking off the rod length each time, is made by drawing the 
arcs A'A, B'B, tangent to the crank circle, from M and N as respective 
centers. Then for any position of C, it is only necessary to draw 
A'CB' parallel to AB, and C will be located on this line just as W is on 
MN; for since the equal lines MA', WC, and NB' are included between 
parallels, they must be parallel; whence A'C = MW. 



A& 



y^- 






w 



Fig. 163. — Piston Travel. 



The analogous construction in Fig. 159 is made by drawing the 
straight-line tangents A' A, B'B: and it appears that the effect of the 
connecting rod is to introduce a curvature into these limit lines. Since 
the straight lines in Fig. 159 may be thought of as arcs of infinite 
radius, the motion there represented is often spoken of as that with 
infinite connecting rod. Another view of the same conception is, that 
if the rod were of infinite length its angular swing would be zero, and 
the piston would receive harmonic motion without distortion. In Fig. 
158, this " infinite rod" is replaced by the simple slide block W, the 
piece which forms the connection between the crank pin and the slide; 
and to carry out the idea still farther, we may think of the surface of the 
slot as a small part of the surface of a wrist pin of infinite radius. 

Example 36. — With a connecting rod five cranks in length, how far is the 
piston from mid-stroke when the crank is vertical, or at 90° in Fig. 163? 

The mid-stroke position of W is at the distance L = nR to the left of 0. 
When C is at G, or a = 90°, OW will be the base of a right triangle of which L 



§ 31 id)] MOTION OF THE ENGINE MECHANISM. 303 



is the hypotenuse and R the other side, so that OW = VL 2 — R 2 = R Vn 2 — 1. 
The distance sought, expressed in terms of the stroke is then 



t- '-y-' g (159) 

Substituting n = 5, we get, 

5 - V24 „ 5 - 4.899 „ n n _ nK „ 
So = S = ^ » = 0.0505$. 

(e) Velocity and Acceleration. — The analytical method will 
be employed first, as it is shorter and gives results in a very useful 
form. From Fig. 163 we get for the travel s the expression 

8 = MW = MO - WO 

= (L + R) - (L cos j8 + R cos a) 

= R(l - cosa:) +L(1 - cos/3); .. . . . (160) 

where the second term, L (1 — cos 0), shows the departure from the har- 
monic motion represented by Eq. (151), or the effect of the connecting 
rod. This is evidently the distance, on the line A'B', between the 
curved limit lines AA', BB' of Fig. 163 and the respective corresponding 
straight lines of Fig. 159. 

To eliminate the rod angle /3, we note that, in Fig. 163, 



whence 



CD = R sin a = L sin 0; 



A R ' 

sin p = -^sin a, 



cos 



(3 = Vl - sin 2 = (l - Tisin 2 a\ 



If this is developed by the binomial formula, the first two terms are 

cos/3 = l -^sin 2 o:+ * * * ; . • • • (161) 

and the succeeding terms, involving high powers of fractions, may be 
dropped without overpassing the limits of desired accuracy. Then 
Eq. (160) becomes 



and from this 



s = R(l — coso;+ y-sin 2 aj; 

ds „ / . . 1 R . n \ da 
v = dt = R { Sma + 2L sm2a )Tt 

= v (sma +-^-sin 2a ) (162) 



304 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 
Likewise 



R \da 
= Vq ( COS a + y cos 2 a J -77 



dv I 

= ~ (cos a + y cos 2 a] (163) 

A strictly exact formula for a in terms of a can be worked out, 
avoiding the approximation of Eq. (161); but it is quite complex, and 
the gain in accuracy is of no practical significance. 

By purely graphical methods, relations which parallel Eqs. (162) 
and (163) may be derived: the first, for piston velocity, will now be 
established, because it is useful in connection with the matter of turn- 
ing force on the crank; but that for acceleration is lengthy in deduction 
and decidedly less convenient in application than constructions based 
upon Eq. (163). 

Example 37. — For a given rod ratio n = L/R, find the crank angle at 
which the piston velocity is maximum. 

Velocity v will be at its maximum when acceleration a is zero. Solving the 
equation 

cos a + - cos 2 a = 0, 
n 

we get 

n cos a + 2 cos 2 a — 1 = 0, 

cos 2 a + £ n cos a = § : 
whence 

cos a = l(V8 + n* -n) (164) 



If, for instance, n is 5, cos a comes out 0.1862 and a is 79° 16'. The sine 
of this angle is 0.9825 and that of 2 a or 158° 32' is 0.3660. Substituting in Eq. 
(162), we have 

v = (0.9825 + 0.0366) v = 1.0191 v . 

(/) Velocity by Geaphical Relations. — It is a fundamental 
principle of kinematics, that if a body has motion in a plane, and if the 
directions of movement of two points of the body are known, the inter- 
section of lines perpendicular to these motion directions determines the 
instantaneous center of rotation — a point about which, at the instant, 
the body is rotating as about a fixed pivot. In Fig. 164, CP and WP 
are drawn perpendicular to the paths (or to the velocity directions) of 
C and W, and P is the instantaneous center. 

If now the connecting rod can be thought of as turning, for the 
instant, about P, the conclusion follows that the velocity of any point 
on the rod is perpendicular to a radius from P to this point, and is propor- 
tional to the length of this radius. The fact that P changes its position 
from instant to instant, or from position to position of the mechanism, 



§ 31 (/)] 



MOTION OF THE ENGINE MECHANISM. 



305 



traveling along a curved path or locus, does not at all invalidate the 
statement just made as to the velocity relations at a particular instant. 




Fig. 164. — The Instantaneous Center of Rotation. 

For the point W only the second of these two relations need be 
used, as the direction of v was part of the data : and we have 

v : v : : PW : PC (165) 

For any other point as E, we first draw a direction line for ve, and 
then find its value by 

v E : v : : PE : PC (166) 

A practical disadvantage of this method is that it involves a lot of 
troublesome graphical work, in the drawing of long lines to get P, and 
in satisfying the proportion (165) or (166). A much more convenient 





Fig. 165. — Velocity Relations. 

construction suggests itself when we note that the line OB, through the 
shaft center O, perpendicular to the stroke line WO, and meeting the 
rod line WC at B, makes a triangle OBC similar to PWC, so that 



v : vo : : OB : OC. 



(167) 



306 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

And if, further, such a scale be chosen that OC = v , then at once 
OB =v. 

The trigonometrical relation between OB and OC is illustrated in 
Fig. 165, which shows parts of Fig. 164 enlarged. In the triangle OBC, 



OB 
OC 



sin OCB sin (a + 0) 



sin OBC 



cos j8 



v 



(168) 



(g) Diagram of Piston Velocity. — In Figs. 164 and 165 are 
shown the two typical conditions, for the first and second quadrants, 
respectively, of the crank motion. In quadrant I, OB/OC is greater 
than sin a, in quadrant II it is less: while for infinite rod, CB would 
be horizontal and the motion symmetrical with respect to the vertical 
line OB. It is not necessary to make a separate determination for the 
lower half of the crank circle, because all kinematic and geometrical rela- 
tions are symmetrical above and below the stroke line. 









G 






c 






D^^Nv 


w^-—^' 


A /-'''" 


F""^ 




9^\ — ^ 




L&J 


L=^r^ 


>./*•*» --Q 








~^k a 










H 



Fig. 166. — Derivation and Form of the Diagram of Piston Velocity. 

In Fig. 166, the radius OC is taken to represent, on a convenient 
scale, the intensity of the (constant) velocity v of the crank pin; then, 
directly from Fig. 165, the rod line WC cuts off, in OD, the length of 
the piston velocity. It is troublesome to be compelled to draw the 
extended mechanism outline OCW in order to get the slant of the rod: 
a far more convenient method is the miniature construction KOL. The 
full radius OC or OL is taken to represent the rod, the short radius OK 
the crank: thus if the rod is six cranks long, OK will be one-sixth of 
OL. In learning to use this device, it is enough to keep in mind the 
general slant of the rod CW; a clear sense of what is wanted is a 
better guide than a formulated rule in the selection of the intersec- 
tions K and L. 

Instead of drawing CD parallel to LO, drop a vertical line CE 
(perpendicular to the stroke line) ; then the intercept CE, equal to DO, 



§ 31 (flf)] 



MOTION OF THE ENGINE MECHANISM. 



307 



will be the velocity v, while CF is the similar quantity for the case of 
harmonic motion. The full-line curve AEOB is the locus of the inner 
end of the ordinate from C for the forward stroke, or for crank arc AGB, 
the dotted curve BOA the corresponding locus for the return stroke, arc 
BHA. The diagram shows very clearly how the connecting rod causes 
the piston to move relatively faster in the first and fourth quadrants, 
slower in the second and third. 

(h) Acceleration of the Slide. — The similar diagram for 
acceleration is based on Eq. (163). Evaluating the factor 

R 



m = cos a + y cos 2 



we have 



ay 



a 



m 



C 
1 + 



R 



90° 

R 

' L 



180 c 



270° 

_R 

L 



Also, for a = 45 deg., 135 deg., etc. 
(that is, for any mid-quadrant crank 
position) m = ± cos a. 

Now in Fig. 167, the radius of the 
circle is a : and for infinite rod it is 
evident that the horizontal distance 
CE', from the C-point to the line GH, 
will give a, according to the relation 
a — do cos a. For the actual mechan- 
ism, GH must be replaced by a curve 
analogous to the D-curve in Fig. 166: 
three points in this curve are got by 
laying off, from m as above, 




Fig. 167. 



R 



^2 H 

Acceleration Diagram. 



OE = GE 1 = HE 2 = j-KO) 

and two more by noting that the curve must cross GH where m = cos a, 
at the mid-quadrant points Ki and K 2 . Without any further deter- 
minations (unless the figure be very large), a fair curve can be drawn 
through these five points which will be the locus of the end of a, 
measured always from C toward the E-curve. 

As indicated in the laying out of points Ei, E , and E 2 , an accelera- 
tion a is considered plus when measured from C to E toward the right 
in Fig. 167, and then acts toward the right. In Fig. 166, an ordinate 
from C down to E is positive, showing a velocity toward the right: the 
opposite direction corresponds with the minus sign in both cases. For 



308 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

crank positions which are symmetrical with reference to AB, the ac- 
celerations are absolutely the same, as for 60 deg. and 300 deg.; but 
referred to the velocities existing at such corresponding positions, these 
accelerations are relatively opposite. 



§ 32. Working Forces in the Engine 

(a) Inertia Force of the Reciprocating Parts. — Knowing the 
acceleration a and the weight W of the sliding parts — which are sup- 
posed to include a portion of the connecting rod — we have only to 
multiply the mass M (equal to W -r- g) by a in order to get the force 
F = Ma required to accelerate this mass, or its inertia force. Then 
for the mechanisms discussed we have, 
For infinite rod, 

n W V 2 fiack\ 

F = — -^cosa; . .- (169) 

g K 

For actual rod, 

F = — V ^(cosa + ^cos2a) (170) 

W v 2 

In either case, ^ is the centrifugal force which the reciprocating 

g K 

mass would have if it were concentrated around the crank-pin center 

C: this ideal centrifugal force will be called F , and the actual inertia 

force is then a component of F , given by 

F = F cos a, (171) 

or by 

F = F (cosa + 2jCOs2a) (172) 

The value of F can be found, for any crank angle, by a diagram 
like Fig. 167, but with F instead of a as the radius. As to direction 



E, G 





H E * "H 

Fig. 168. — Circular Diagrams of Inertia Force. 

of force, it must be remembered that accelerating force will point 
toward the center O or toward the limit line GH or EiE E 2 ; while 



§ 32 (a)] 



WORKING FORCES IN THE ENGINE. 



309 



inertia force will point outward, or away from the middle of the dia- 
gram. This is illustrated in Fig. 168, where the two cases as to form 
of mechanism are separated, the two diagrams embodying Eqs. (171) 
and (172), respectively. 

These diagrams are not, however, in a shape suitable for the direct 
combination of inertia force with steam pressure, since the latter, given 
by the steam diagram, is laid out on a stroke-line base The derivation 
of an inertia diagram in these terms is shown in Fig. 169, where, in I, 




Fig. 169. — The Stroke-line Diagram of Inertia Force. 



the diagram from Fig. 168 II is surrounded by another diagram, for 
piston position, like Fig. 163. From this we get the two coordinates 
for the curve in II, the abscissa 5 = MS at FC, the ordinate F = ST 
at CE. For the actual mechanism this gives the curve PQR, for in- 
finite rod, the straight line JKL. It must be clearly understood that 
this is a diagram for both strokes, as is indicated by the numbered 
positions on both figures. The meaning of plus and minus (up and 
down) ordinates in II is shown by the arrows. 

That JL must be a straight line is evident when we consider that, 
with infinite rod, the distance SK from mid-stroke and the inertia force 
F are both proportional to cos a. With the curve, the areas PMQ, 
QNR — the first representing work stored in the moving parts from 
zero velocity to maximum, the second that given back during retarda- 



310 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

tion — must be equal. Note that the dead-center acceleration is 
always greater than a Q at the head end and less at the crank end, the 
ends being taken according to the conventional arrangement in Fig. 162. 

As written Eqs. (171) and (172) give the total inertia force in the 
engine. For combination with steam-pressure diagrams it is usually 
desirable to have the force per square inch of piston, so that F /A 
and F/A are more commonly dealt with than F and F. 

As regards the division of the mass of the connecting rod, for " con- 
centration" at the pins — see § 30 (c) — to put one-half at each center 
serves very well when the driving force is in question. It is more logical, 
because strictly correct when the result sought is the total " shaking 
force" of § 30 (/), to use the division got by weighing the two ends on 
knife edges at or under the axes of the pin bearings. This keeps the 
center of gravity of the rod unchanged: thus if the center is at 0.6 of the 
distance from wrist pin W to crank pin C, 0.6 of the mass goes to C r 
0.4 to W. 

Example 38. — A 14 in. by 15 in. engine, which runs at 250 r.p.m., has a 
connecting rod 42 in. long, and the total reciprocating weight is 325 lb. Find 
/''o and Fo/A, also the value of F/A at the dead centers and at 50° and 125° of 
crank angle. 

From Example 35, the centripetal acceleration ao of the crank-pin center is 
428.4 ft. per sec. per sep. Then the ideal centrifugal force is 

ft -gq.- 325 *^ ., 4329 lb. 

g 32.16 

The area of the 14 in. piston is A = 153.9 sq. in., so that 
^-° = 4329 ^ 153.9 = 28.12 lb. per sq. in. 

Here ■=- = -— = -— ; then at head-end dead center, 

L 42 5.6 

?r = 28.12 + ?|P = 28.12 + 5.02 = 33.14 lb.; 
A 5.6 

and at the crank-end dead center, 

£ = 28.12 - 5.02 = 23.10 lb. 
A 

Now evaluating m = ( cos a + j cos 2 a J , we have at 50°, 

m = 0.6428 - u 'J = 0.6428 - 0.0310 = 0.6118; 
5.6 



and at 125°, 

Then the required values of F/A are, 17.20 lb. at 50° and -17.85 lb. at 125°. 



m = -0.5736 - 5^9 = -0.5736 - 0.0611 = -0.6347. 
5.6 



§ 32 (&)] 



WORKING FORCES IN THE ENGINE. 



311 



(6) Effective Driving Force. — In Fig. 170 a pair of indicator 
diagrams, from the two ends of the cylinder, is shown at I: and by 
means of motion arrows the fact is made clear that the forward-pressure 
line, or steam line of one end, as AB, is simultaneous with the back- 
pressure line, or exhaust line of the other end, as GH. Then a sub- 
traction of Pb from Py for the whole of each stroke, giving Pe — refer to 
Fig. 153 — is made by the combination in II; where MGHN (crank 
end) is superimposed on MABN (head end), and where the effective 




Fig. 170. — Effective Driving Force. 

steam pressure Pe is given by the ordinate intercepted between the 
curves AB and GH. Note that whereas the indicator cards in I are 
for the two ends of the cylinder, the two diagrams in II are for the re- 
spective strokes (compare § 21 (6): and further that, with high com- 
pression, the back pressure will rise above the forward pressure toward 
the end of each stroke, so that the mechanism will have to drag the 
piston to dead center instead of being driven by it. In § 30 (b), the 
pressures Pf and Pb were defined as absolute pressures, above perfect 
vacuum; as shown in Fig. 130, on diagrams from a noncondensing 
engine, they are measured above atmosphere: but since their difference 
is the result sought, either datum line may be used. 

The diagrams in Fig. 170 II, where the variable ordinate p s is 
included, between curves, are brought to a more convenient form in 



312 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

Ill, by measuring the ordinate up (and down) from MN, and getting 
the p E -diagrams MABCN, NEFGM, on straight base lines. The 
inertia-force diagram can be combined directly with these by laying it 
off on the same base line — being inverted for the return stroke be- 
cause the direction of positive or forward-acting steam pressure is there 
reversed. This shows clearly how the inertia force diminishes the 
effective pressure during the first part of each stroke and increases it 
toward the end — an action which, with the usual form of indicator 
diagram, greatly favors a uniform distribution of driving force and of 
transmitted work throughout the stroke: in this particular case, the 
negative pressure toward the end of the stroke, without inertia, is almost 
entirely eliminated when the latter is taken into account. 



Head. ^"X 


-100 


js Crank. 


D \ 


-80 / 
-60/ 


H 


V^""""^^ 


-40\^^ 
-20 


^ ^B / 


^1g ^- 


~ 


^ c\ 







M N 

Fig. 171. — Indicator Diagrams from Fig. 84. 



(c) The Double Diagram of Driving Force. — To illustrate an- 
other method of combination and to serve as a basis for some further 
determinations, the diagrams in Fig. 84 are brought to a common base 
line in Fig. 171, reversed into the standard position and with irregular- 
ities due to the indicator smoothed out. Effective steam pressures can 
now be measured directly from this double indicator diagram, between 
curves AB and GH for the forward stroke, between EF and CD for the 
return stroke. These intercepts are laid off from the straight-line 
base in Fig. 172, forces acting toward the right being measured upward 
and those toward the left downward. Since now there is only one 
direction meaning of the ordinates, a single inertia curve serves for 
both strokes: to get effective driving force at wrist pin, measure from 
PQR to ABC for the forward stroke and to DEF for the return stroke. 

In a vertical engine, the weight of the reciprocating parts acts as a 
constant force in the direction of their movement, increasing driving 
force in the down stroke, diminishing it in the up stroke — the cylinder 



§ 32 (c)] 



WORKING FORCES IN THE ENGINE. 



313 



being, of course, above the shaft. In Figs. 170 III and 172, this can 
easily be taken into account by a simple shifting of the base line MN 
(and with it the inertia curve) through a distance equal to W/A. 

It is apparent that the inertia-force action of these moving masses 
tends to equalize the distribution of driving work, storing up the ex- 
cess in the first part of each stroke and delivering it in the latter part, 
when the effective steam pressure has fallen low or even reversed in 
direction. 



joo 




Fig. 172. — The Two-stroke Diagram. 

(d) Turning-force Relations. — Two methods of reasoning may 
be followed in finding, for a known driving force at the wrist pin, the 
turning effect upon the crank: both are under the assumption that the 
connecting rod is a weightless transmitting link, its inertia having been 
taken into account according to § 30 (c). The first is illustrated in 
Fig. 173, where the force *S transmitted along the rod is the resultant 
of the driving force P and the guide reaction Q. The perpendicular OE 
from upon the rod line is the lever arm of this force, and its moment 
is 

M = SX OE. 

Drawing also the vertical line OB, we have that the triangles OEB, 
WFH, are similar: wherefore 

P : S : : OE : OB, 



314 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



or 



PXOB = £XOE = .M: 



(173) 



and the turning effect is just as though the force P acted upon the 
crank with the lever arm OB. 

In the mechanism of Fig. 158, or with "infinite connecting rod," 
the force P would be applied horizontally, or parallel to the stroke 
line, at C, and its lever arm would be CD "or R sin a: the increase of 
arm length from CD to OB measures the effect of the connecting rod. 
In the second quadrant, OB will be less than CD. 




Turning-moment on the Crank. 



Replacing the moment M in Eq. (173) by that of a tangential 
force T at C, with the arm R, we have 

M = PX OB = TXR, 



or 



^ = OB xp = sin (a + 0) p. 



(174) 



R cos p 

the geometrical relation being the same as that for the velocities in 
Fig. 165, and Eq. (174) derived like Eq. (168). The relation 

v ~ P 



(175) 



which comes from a combination of these two equations, is necessarily 
true from fundamental principles. Under the assumption of no fric- 
tional or internal losses in the machine, work rate at wrist pin must 
equal work rate at crank pin. This rate is equal to the product of 
working force by its velocity (along the force line); therefore the 
equation 

vP = v T (176) 

must be true. 

The second derivation of T is through force analysis strictly, and is 
shown in Fig. 174. Here the rod force S is carried over to C and there 
resolved, as suggested in Fig. 153. From triangle WFH or CED, 

P 



S = 



cos/3' 






§ 32 (d)] 



WORKING FORCES IN THE ENGINE. 



315 



and in triangle CGD, right-angled at G, and with angle CDG = angle 
OCD = (a + 0), 

T = Ssin(« + (3) = P sin ^+^) . .... (177) 

cos fi 

If we apply to this expression the effect of making the rod infinite — 
which makes /3 zero — we get at once the simple relation indicated by 
the lever arm CD or R sin a in Fig. 173, namely, 



T' = Psina; 



(178) 



which is, of course, the same as the velocity relation for that mechanism, 
inEq. (152). 




Fig. 174. — Tangential Force on Crank. 



(e) Determining Tangential Force. — Having drawn the dia- 
grams of effective driving force, like Fig. 170 III or Fig. 172, and 
located on them a series of ordinates corresponding to a number of 
equally-spaced crank angles, the next step is to find the turning force 
T for each of these P's. One method, shown and used in Fig. 175, is a 
direct application of the relation expressed in Eq. 174), which is 
equivalent to 

T : P : : OB : OC (179) 

on Fig. 174: and the construction is similar to that for v in Fig. 166. 
The crank circle on AB is of any convenient size, but with its radius 
greater than the largest value of P on the diagram of effective driving 
force. Each length of P, taken from Fig. 170, is measured inward 
along the corresponding crank line, as CD; and the length CE, cut from 
the vertical by DE parallel to the rod line, is T. The triangle CDE 
is similar to OCB in Figs. 173 and 174; and the construction in Fig. 
166 is used for finding the rod angle. A separate triangle must be 
drawn for each crank position. The T's, when found, are laid off 
radially outward from the circle, and a curve is traced through their 
ends. 



' 



316 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



Table 15. Turning-Force Ratios. 

Values of m = ^— - — - = ^ = — , for different values of n 

cos 13 P Vq 



L 

R 



_c 




Values of n. 


ct 


4 


5 


6 


8 


00 


5 


355 


.1089 


.1045 


.1016 


.0980 


.0872 


10 


350 


.2164 


.2079 


.2022 


.1950 


.1737 


15 


345 


.3215 


.3089 


.3005 


.2901 


.2588 


20 


340 


.4227 


.4065 


.3957 


.3822 


.3420 


25 


335 


.5189 


.4995 


.4866 


.4706 


.4226 


30 


330 


.6091 


.5870 


.5724 


.5542 


.5000 


35 


325 


.6923 


.6682 


.6523 


.6325 


.5736 


40 


320 


.7675 


.7421 


.7253 


.7054 


.6428 


45 


315 


.8341 


.8081 


.7910 


.7699 


.7071 


50 


310 


.8915 


.8657 


.8488 


.8279 


.7660 


55 


305 


.9392 


.9144 


.8982 


.8782 


.8192 


60 


300 


.9769 


.9540 


.9390 


.9205 


.8660 


65 


295 


1.0046 


.9842 


.9709 


.9545 


.9063 


70 


290 


1.0224 


1.0051 


.9939 


.9801 


.9397 


75 


285 


1.0303 


1.0169 


1.0082 


.9974 


.9659 


80 


280 


1.0289 


1.0197 


1.0137 


1.0064 


.9848 


85 


275 


1.0186 


1.0139 


1.0109 


1.0072 


.9962 


90 


270 


1.0000 


• 1.0000 


1.0000 


1.0000 


1.0000 


95 


265 


.9738 


.9785 


.9815 


.9853 


.9962 


100 


260 


.9407 


.9499 


.9559 


.9633 


.9848 


105 


255 


.9015 


.9150 


.9237 


.9344 


.9659 


110 


250 


.8570 


.8742 


.8855 


.8992 


.9397 


115 


245 


.8080 


.8284 


.8417 


.8581 


.9063 


120 


240 


.7552 


.7781 


.7931 


.8116 


.8660 


125 


235 


.6991 


.7239 


.7401 


.7601 


.8192 


130 


230 


.6406 


.6664 


.6833 


.7042 


.7660 


135 


225 


.5801 


.6061 


.6232 


.6444 


.7071 


140 


220 


.5181 


.5435 


.5603 


.5810 


.6428 


145 


215 


.4549 


.4790 


.4949 


.5147 


.5736 


150 


210 


.3909 


.4130 


.4276 


.4458 


.5000 


155 


205 


.3263 


.3458 


.3586 


.3747 


.4226 


160 


200 


.2614 


.2776 


.2884 


.3018 


.3420 


165 


195 


.1962 


.2088 


.2171 


.2276 


.2588 


170 


190 


.1309 


1394 


.1451 


.1523 


.1737 


175 


185 


.0654 


.0698 


.0727 


.0763 


.0872 






A second method uses the computed values of the ratio of T to P, 

or of m = — - — , given in Table 15, working through a reduction 

cos j8 

or proportion diagram like those in Fig. 81. The base line AB, Fig. 176, 

is taken of any convenient length, and along the perpendiculars AC 



§ 32(e)] 



WORKING FORCES IN THE ENGINE. 



317 



and BD are measured values of m X AB. Note that m rises from 
zero to a little more than 1.00, then comes back to zero at the other 
dead center. To avoid overlapping of the ascending and descending 




Fig. 175. — Turning-force Diagram. 

series of lines, values belonging to quadrants I and IV are laid up on 
AC, those for quadrants II and III on BD. Then the inclined lines 
are drawn: and for any particular crank angle, as20deg., we have only 




G B^r^4 

Transformation Diagram. 

to measure off from B, as BG, the length of P taken from its diagram, 
in order to get the corresponding T in GF. 

(/) Diagrams of Turning Force. — Values of T having been de- 



318 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

termined, they can be laid out either from the crank circle, as in Fig. 
175, or from a straight-line base, as in Fig. 177. This latter base line 
is the developed crank circle : that is, the upper and lower halves of the 
circular diagram are straightened out and brought together. The cir- 
cular diagram is clearer for illustrating the continuous variation in 
turning force, while the other is better for quantitative determinations. 
Assuming that the load on the engine is a uniform torque, and 
either that there are no frictional losses or that their effect is included 
in the load, we get the value of the equivalent resistance at the crank 
circle by finding the mean tangential force through Eq. (150). Measur- 
ing off this T m at AK, we draw the resistance circle KL on Fig. 175: 
and by comparing the curve of actual turning force, AQRBST, with 
this circle of uniform resistance, we get an idea of the duty which the 
fly wheel has to perform. Only at four points, Q, R, S, and T, is the 




Fig. 177. — Diagram on Developed Circle. 

driving force just equal to the resistance: during two periods or phases, 
marked I and III, the work done upon the shaft is less than that 
taken from it, and the deficiency is supplied by energy from the wheel, 
which of course slows down; but during phases II and IV the wheel 
has to store up excess work, and regains kinetic energy. Knowing the 
largest amount of work to be taken care of by the wheel, as shown by 
the diagram, and the greatest permissible variation of speed within the 
revolution, we can compute the weight of wheel rim required under any 
conditions. 

(g) Fly-wheel Data. — Both forms of the turning-force diagram, 
Figs. 175 and 177, show force plotted on a distance base: but only in 
the straight-base diagram, where the ordinates are parallel, is work 
truly represented by area. Working then on Fig. 177, we can get the 
data for fly-wheel determination in several forms. 



§ 32 (g)] WORKING FORCES IN THE ENGINE. ■ 319 

Measuring the area of each phase and dividing area in square inches 
by base in inches, we get the mean height and reduce it to the pressure 
scale: note that the bases of the broken phases I and III in Fig. 177 
are KQ + K'T, RL + SI/. Besides this, the four phase lengths are 
to be expressed in degrees, so as to measure the angles TOQ, QOR, 
ROS, SOT in Fig. 175. Let 

7 = this phase angle, in degrees; 
I = length of phase, on crank circle, in feet; 
t = average unbalanced force acting during phase, in pounds per 

square inch of piston, so that At is the total force for the 

engine; 
E = work value of the phase, in foot-pounds. 

The circumference of the crank circle is 

C = f|ft.; 

then l = m> Citm ' and E = tAlit lb (180) 

Again, in Fig. 177, the whole area of the diagram AGBH, or the 
equivalent rectangle KLL'K', represents the work of the engine in one 
revolution, which we may call Wr: and if we find the ratio k which each 
phase area bears to the total area, we can get E through the relation 

E = kW R (181) 

If we know the average m.e.p. or p m , we find Wr by 

W R = 2^A Pm (182) 

Or, having the i.h.p. H and the r.p.m. N, 

Wr= 33W0H (lg3) 

Finally, knowing the dimensions of the engine and the scales used 
in laying out Fig. 177, we may calculate a work scale of foot-pounds 
per square inch, as follows: 

Suppose that Fig. 177 is drawn for a 14 in. by 15 in. engine, and 
that in the figure the circumference scale is 1 in. = 20 deg., while that 
for pressures is 1 in. = 24 lb. per sq. in. Then the circumference of the 
15 in. crank circle is 3.927 ft., and the distance value of 1 in. along the 
base of the diagram is 

^ X 3.927 = 0.2182 ft. 



320 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

The piston area being 153.9 sq. in., the total force value of 1 in. of ordi- 
nate is 24 X 153.9 = 3694 lb. : so that 1 sq. in. represents 

0.2182 X 3694 = 806.0 ft. lb (184) 

A table of data from Fig. 177, applying it to an engine 14 in. by 

15 in. at 250 r.p.m., is shown below. With the degree scale 1 in. = 20 

deg., the length of the diagram must be 9 in.: the measured area of the 

whole figure AGBH was 23.17 sq. in.: so that the mean turning force 

or m.t.f. is 

93 17 
^m = ~g^ X 24 = 30.9 lb. 

Applying Eq. (150) backward, the m.e.p. corresponding would be 

P m = 30.9 4- 0.6366 = 48.5 lb., 
as against an average value of 48.03 on page 164: the discrepancy is 
due to inaccuracy in measurement and transference of the small indi- 
cator diagrams. 

Table 16. Results from Fig. 177. 



Phase No. 


Area, sq. in. 
a 


Angle, 

degrees. 

• 7 


Length, 

feet. 

1 


Mean force. 
t 


Phase-ratio. 

ifc 


Work-value. 
E 


I. 

II. 

III. 

IV. 


-3.34 
+3.92 
-4.23 
+3.67 


70.6 

95.0 

91.0 

103.4 


0.770 
1.036 
0.993 
1.129 


-23.4 
+19.4 
-22.3 

+17.0 


.1442 
.1715 
.1824 
.1584 


-2690 
+3160 
-3410 
+2960 



In Table 16, the phase areas a were measured with the planimeter, 
as was that of the whole figure: given as measured, they check by add- 
ing up very nearly to zero. Dividing each by its base in inches, and 
multiplying by the force scale 24, gives the mean force t. The phase 
angles y were measured with a scale of 20 to the inch and made to add 
up to 360 deg. : and the corresponding lengths I on the crank circle were 
got by multiplying y by the value of 1 deg. in feet, which is 3.927 -5- 
360 = 0.01091 ft. The phase area a divided by the total area 23.17 
sq. in. gives the ratio k. Finally, E is got from a through the work 
scale of Eq. (184). 

The work per revolution, Wr, as found from the total area 23.17 

sq. in., is 

W R = 23.17 X 806 = 18,650 ft. lb. 

By Eq. (182) it is 

Qf) 

W R = ~ X 153.9 X 48.5 = 18,650 ft. lb. 



§ 32 (g)] WORKING FORCES IN THE ENGINE. 321 

The supply of data in this table is redundant, more being given 
than is necessary for the solution of any particular problem. It will 
be noted that a, 7, t, and k depend only upon the form of the diagram, 
while I and E involve also the dimensions of the engine. 

§ 33- Fly-wheel Action 

(a) Weight of Wheel. — The variation work E, just determined, 
is to be taken up or given off by the wheel within a certain prescribed 
limit of speed change. This limit is generally defined by stating that 
the range from the greatest velocity Vi to the least velocity V2 of the 
wheel rim is not to exceed a certain fraction / of the average velocity 
V. The change in kinetic energy of a mass whose weight is W, in a 
drop of speed from V\ to V 2 (or the reverse), is 

W (7l 2 _ y 2 2) w (Vl + y 2 ) 
E-- j (7x - 70 

W WV 2 

= -XFX/7=/— (185) 

9 9 

This E is identical with that in Eqs. (180) and (181) : so that the method 
of solving the fly-wheel problem consists in getting from the diagram 
an expression for, or value of, the work to- be taken care of by the 
wheel, and equating this to the expression for change in kinetic energy. 

The fraction / of permitted fluctuation varies with the character of 
the work done by the engine: a good degree of uniformity, suitable for 
ordinary high-grade work such as driving electric generators and tex- 
tile mills, is secured by making / = about 0.01. In slow-running en- 
gines on rough work, the fluctuation often greatly exceeds this value, 
rising to 5 or 10 per cent or more; while in the work requiring the 
greatest delicacy of regulation — the driving of alternating-current 
generators in parallel — the fly wheel must be very powerful. 

It must be clearly understood that the regulation of the speed 
within the revolution, by the fly wheel, is a different matter from the 
regulation of the average speed by the governor, through a continuous 
accommodation of the power of the machine to its load. 

Example 39. — Find the weight of fly wheel at an effective radius of 36 in. 
which will regulate the 14 X 15 — 250 engine of Fig. 177 within 1 per cent. 
Circumference of wheel = 6 X 3.1416 = 18.85 ft. 

Velocity of rim = 18.85 X ^ = 78.54 ft. per sec. 

60 

V 2 6169 

J_ = £^ = 191.8; / = 0.01. 

g 32.16 ' J 



322 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

From Table 16, the greatest value of E is 3410 ft. lb.; then for W we get by 
Eq. (185) 

If this all goes into the rim, and we make the latter 12 in. wide, with cast 
iron at 450 lb. per cu. ft. the rim would be about 2.5 in. thick. 

Example 40. — An engine 24 in. by 48 in. at 80 r.p.m., has a wheel 18 ft. 
in diameter and weighing 12,500 lb. How close will be the regulation if the 
m.e.p. is 40.2 lb. and the phase ratio k is 0.16? 

The work per revolution is 

W n = 2 X 4 X 452.4 X 40.2 = 145,490 ft. lb. 
The work to be absorbed by the wheel is then 

E = 145,490 X 0.16 = 23,280 ft. lb. 
The velocity of the rim is 



Then 
and 



SO 
V = 56.55 X gQ = 75.40 ft. per sec. 

F 2 5685 17AQ 

~ = ooTa = 176 ' 8 
g 32.16 

/= 12,5(?xT76.8 - 001056 - 



(6) Effective Radius of Wheel. — A mass particle m, at the end 
of a radius r which makes n turns per second, has the kinetic energy 

e = —±— = 2ir 2 mr 2 n 2 (186) 

The total kinetic energy of the fly wheel, the summation of the e's of 
all the particles, will then be equal to the product of a constant by 

I mr 2 . wmcn integral is the polar moment of inertia of the mass of the 

wheel about its rotation axis. As always in such a case, an equivalent 
effect would be got by imagining the whole mass of the wheel to be con- 
centrated in a ring at the end of the radius of gyration : then this radius 
of gyration is the effective radius of the wheel, for which the velocity 
V in Eq. (185) is to be calculated. 

Usually, the rim of the wheel contains by far the greater part of its 
mass, and the parts near the shaft, at short radius, have very little 
value as energy vehicles; so that no great error is caused, especially 
with wheels of the belt-pulley shape, by taking only the rim of the 
wheel into account, and using that as if concentrated at its outer cir- 
cumference. 

When, however, great accuracy is required, the polar moments of 
rim, arms, hub, and crank discs can be approximately computed and 
an equivalent mass at the outer radius found. And when there are 



§ 33 (&)] 



FLY-WHEEL ACTION. 



323 



other rotating bodies attached to the shaft, as for instance the arma- 
ture of a generator, these also must be reduced to the wheel rim. The 
relation through which this reduction is made is that the energy value 
of any mass varies as the square of its radius from the axis, or that the 
mass for any energy value is inversely as the square of the radius. 

(c) Multiple-crank Arrangements. — Besides using a fly wheel 
to restrain the fluctuations in speed due to irregularity in turning force, 
there is another method of securing uniformity of running: this con- 
sists in the use of two or more cranks at angles with each other (that is, 
not opposite, or at 180 deg). Then the excess phase of one crank can be 
made to coincide with the deficiency phase of the other; and not only 
will there be no dead center, so that the engine will start from any 
position, but there will be a much smaller variation in the total turning 
force or turning moment on the shaft. The freedom from dead centers 
is especially important in engines that have to start frequently against 
their full resistance, as locomotives, hoisting engines, and the like: and 
these are always made duplex, with cranks at right angles. Of course, 
a compound engine, with each cylinder driving its crank, will have the 
same action: except that in engines of the locomotive class, provision 
must be made for admitting steam directly to the low-pressure cylinder 
at starting, without waiting for it to get through the high-pressure 
cylinder. 




Fig. 178. — Circular Diagrams Combined. 

An example showing the simplest case of this combined action is 
given in Figs. 178 and 179, which represent the working of a duplex 



324 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

simple engine with cranks at right angles. The two turning-force 
curves are supposed to be alike, and are taken from Fig. 175. The sec- 
ond crank will be at dead center when the leading crank is at 90 deg., 
hence the location of A 2 and B 2 on the drawings. The resultant curve 
of total turning force is got by adding the ordinates of the simple curves. 
The circle or line of total resistance is drawn on the resultant curve, 
and it at once appears that the variations in driving force on the crank 
pin are much smaller, especially in comparison with the mean force, 
than in a single engine. The form of curve here shown, with a mini- 
mum at each quarter-point and a maximum near the middle of the 
quadrant, is characteristic of this type of engine. 




90 180 270 

Fig. 179. — Turning Force in Quarter-crank Engine. 



360 



In the larger multiple-expansion engines, with three or four cranks, 
especially in marine engines, there is a considerable variety in the 

arrangement of the cranks, as to angles 
and as to order of sequence. Combined 
turning-force diagrams for these engines 
are made in the same manner as Fig. 
178 or 179. An additional complica- 
tion is encountered, in that the pistons 
are not of the same size; so that if the 
separate curves are to be combined, they 
must either be worked out for total force 
on crank, or else one piston must be 
taken as the chief and the pressures on 
the others be referred to that one, or 
be expressed as equivalent pressures per 
unit of area of that piston. 
(d) Stress in Rim of Wheel. — The simplest possible problem as 
to the load imposed by centrifugal force is represented in Fig. 180, 
where the rim is considered a plain, homogeneous ring, the radial ten- 




Fig. 180. — Centrifugal Force on 
Wheel-rim. 



§ 33 (d)] FLY-WHEEL ACTION. 325 

sion of the arms being left out of account. The force tending to 
cause rupture at any section as AB, and resisted by tensile stress in the 
ring, is found by getting the value of the resultants Fi, F h each of 
which is the sum of the components, at right angles to AB, of all the 
radial forces on the particles of the half ring. The mathematical de- 
duction of the value of this resultant force is as follows : 

Let a be the area of cross section of the rim in square feet, I any 
length in feet measured along its circular center line, and w the weight 
per cubic foot of the material. Then the centrifugal force of a piece of 
unit length will be 

f = j V i-- <**> 

and for an element of the length dl = Rda, we have 

dF = fdl = fRda. 

Now the component perpendicular to AB is df sin a, so that 

dF i= fR sin a da: 

and integrating for the half circle we get 

F 1 =fR f" sin a da = 2 fR (188) 

The total centrifugal force on the half rim is 

iF = TfR; 

and we see that the bursting tendency is as if the force/ were distributed 
along a bar of length equal to the diameter of the wheel, and that the 
force Fi bears to the whole centrifugal force F of the rim the ratio 1 : x. 
This load is taken up at two sections of the rim, so that the ten- 
sion at either section is F/2 x. 

Example 41. — A wheel 16 ft. in diameter, with rim 24 in. wide by 3 in. 
thick, is made in sections and bolted together with five If in. bolts at each 
joint: what will be the tensile stress in the cast-iron rim and in the bolts, on 
account of centrifugal force at 100 r.p.m., disregarding any holding effect which 
the arms may exert? 

Using the mean diameter 15.75 ft., the velocity of the rim at 1.667 rev. per 

sec. is, 

V= 3.142 x 15.75 X 1.667 = 82.47 ft. per sec. 



By computing the value of 

V 2 6801 



- 26.86, 



gR 32.16 X 7.875 
we see that the centrifugal force on each pound of rim mass is 26.86 lb. 



326 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

The weight of the rim is, 

w _ 3 X 24 X 3.142 X 189 X 450 _ - 1 - - ft „ 
W 1728 U ' 15U lb ' 

And the tension on the rim is then 

T :_ 1MMX2&86 = 47 ' 6001b . 

0.283 

On the 72 sq. in. of rim section this brings a stress of only 681 lb. per sq. in. 
On the five bolts, of an effective diameter (under the threads) of 1.25 in. and 
with 1.23 sq. in. of cross section, the stress will be 



S = 



47,600 ---„ 1K 
I ^ r5 = 77501b.persq.m. 



(e) Limit of Speed. — Manifestly, the analysis just exemplified is 
far from complete. In every wheel, the arms exert more or less radial 
tension, and the rim has some tendency to bend or bulge outward be- 
tween them; the resulting bending stresses are accentuated when there 
are joints between the arms, especially with a thin rim. An attempt at 
a complete determination of stress, necessarily complicated and at the 
best only approximate, belongs to machine design rather than to the 
present course. However, in terms of the very simple assumption of 
Fig. 180, an important general relation between linear velocity and 
stress in the rim may be established. 

Multiplying both sides of Eq. (187) by the circular length irD of the 

ring, we get 

F = <jrDf= 2ttR — %■ • (189) 

g K 

Taking out the factor 2 w, we have the tension T and can equate it to 
the expression for the strength of the ring, getting 

T=—V 2 = lUaS: (190) 

Q 
from which 

V* = ~^-S (191) 

It will be noted that in Eq. (189) the volume factor 2 ttE was necessarily 
in feet, while S is in pounds per square inch ; and if we take a in square 
feet and w in pounds per cubic foot, the factor 144 must be introduced, 
as above. 

For cast iron, with a maximum allowable working stress of, say, 
4000 lb. per sq. in., the greatest safe speed would be 

T/ 4 / 144 X 32.16 X 4000 9n _, + 

V = y jcrv = P sec * 



§ 33 (e)] 



FLY-WHEEL ACTION. 



327 



While for a high-grade steel, where S might be as much as 20,000 lb., 
the value of V would be about 200 X V5 = 450. This is greatly ex- 
ceeded in turbines of the De Laval type; but there the radial tension of 
the solid wheel becomes a principal element of strength. 

The reason for the disappearance of R from Eq. (189), expressed in 
other than purely mathematical terms, is that while, for a given linear 
velocity V, the centripetal acceleration varies inversely with the radius 
R, on the other hand the weight of a ring of given cross section increases 
as R. 

Because of uncertainties as to homogeneity of construction, to- 
gether with unavoidable irregularities in the distribution of stress, it is 
usual to consider 100 ft. per sec. as about the safe limit of speed for the 
rims of ordinary engine wheels. 



§ 34. Pressures on Pins and Bearings 

(a) Approximate Pressures on the Pins. — In Fig. 181, as here- 
tofore, it is assumed that the mass of the connecting rod is divided into 




Fig. 181. — A Simple Determination of Pin Pressures. 

two parts and concentrated at or around the pins. The portion at the 
wrist pin may be added to the slide mass and given its effect in de- 
termining the resultant driving force Pd- The rod, being now an ideal 
bar without mass, can have force acting only along its center line; 
wherefore the resultant of Pd and of the guide reaction Qg must lie 
along the line WC. Up to this point, the diagram is identical with 
Figs. 173 and 174; but when the rod force S is carried over to the crank 
pin, instead of finding its moment or resolving it, we combine it with the 
centrifugal force Pc of the rod mass around the crank pin. The re- 
sultant is the pressure Pc on that pin. 

A closer analysis of conditions at the wrist pin is made at A, Fig. 
181. The driving force Pd is determined by the inertia of the purely 
sliding parts, the rod inertia Pw being kept separate. Center-line force 
S and inertia Pw combine to produce the pressure Pw of rod on wrist 



328 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

pin; and the resultant of Pt> and Qg must be the equilibrant of that 
pressure. 

In Fig. 172, the value of F /A is 36 lb., due to a reciprocating mass 
which includes half the rod. Of the total weight of reciprocating parts, 
a good average assumption gives the piston slide 0.6 and the connect- 
ing rod 0.4: then one-half of the rod equals one-third of the slide, and 
out of a total of 36 lb. the half rod will have a centrifugal force of 9 lb. 
per sq. in. of piston. 

(b) Pressure Diagrams. — Fig. 182 shows successive pressures on 
the crank pin, got by the method of Fig. 181. At any particular posi- 




270 



Fig. 182. — Diagram of Crank-pin Pressures. 

tion, the line CE is the force S along the rod (found from the values of 
Pd in Fig. 172) and ED is the centrifugal force Fc, so that CD is the 
pressure Pc of the connecting rod upon the crank pin. It will be noted 
that some of the D points are double: in reality the full CD lines in 
this figure were found by an exact method, with a true determination 
of the inertia of the rod; and the fact that the discrepancies between 
the D points at the ends of the CD lines and those at the ends of the 



34 (&)] 



PRESSURES ON PINS AND BEARINGS. 



329 



ED lines are scarcely visible is an ample proof of the sufficiency of the 
approximate method. Note further how the rod inertia Pc combines 
with the slant of the rod, in such fashion as to throw the pin pressures 
farther from the direction of the stroke line throughout the forward 
stroke, but to bring them almost into parallelism with it during the 
return stroke. 

The simplest form of pin-pressure diagram, correct enough for all 
purposes of machine design, is given in Fig. 183. The effective steam- 




Fig. 183. — Approximate Pin Pressures. 

pressure curves ABC and DEF are the same as in Fig. 172. By draw- 
ing the inertia-force curve ST for the slide alone, or for Fo/A = 27 lb. 
in this particular case, we get Pd as at A in Fig. 181, and this is practically 
the same in length as the wrist-pin pressure Pw- Again, drawing curve 
UV for the inertia of the slide plus the whole rod (for F /A = 45 lb.), 
we get the horizontal component of the crank-pin pressure Pc. Of 
course, ordinates are to be measured from ST or UV to the steam 
curves in either case. Inspection of Fig 182 shows that the difference 
between the crank-pin pressure and its horizontal component becomes 
relatively quite large when the pressures are small: but the values of 
the larger pressures are very closely given by the ordinates of Fig. 183. 
(c) Reversal of Driving Force. — Fig. 184 is intended to illus- 
trate the effect of compression, and also of inertia, in causing less 
abrupt reversal of force in the engine and thus producing smoother 



330 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

running. The same forces are shown as in Fig. 183, but the base is 
changed to the developed crank circle, or the diagram is on a time base. 
In the plot of the effective steam-pressure curve, the vertical lines 
at CD and FA are reproduced from the stroke-line diagram (with ap- 
parently instantaneous change of pressure); but the actual manner of 
pressure rise in the filling of the clearance space will be as indicated by 
the short dotted curves. If there was no compression, the line of 
steam-force variation, toward and past the dead center, would be of 




Fig. 184. — Developed Diagram of Horizontal Pin Pressures. 

the form sketched at GHK and JLP. The speed of the pressure -rise 
(from H to K and from L to P), and its exact timing in the cycle of 
the engine, would depend very much upon valve action in relation to 
volume of clearance; but it is quite sure to be much more rapid than the 
rise of back pressure caused by compression. 

It is often said, rather loosely, that the mechanical effect or ad- 
vantage of compression is "to bring the reciprocating parts quietly to 
rest," or "to absorb the shock of the reversal of motion." Neither ex- 
pression is correctly descriptive. There is nothing of the nature of a 
"shock" in the smoothly fluctuating inertia force of the reciprocating 
parts; and while passing the dead centers this force is varying less 
rapidly than in any other part of the revolution. The spreading of the 
pressure reversal over a longer time, making it less abrupt and thus 
decreasing the tendency to shock in the taking up of any slack or loose- 
ness which may exist in the joints, is the true gain from . cushioning by 
compressed steam. Further, as appears from the more exact repre- 
sentation of the crank-pin pressures in Fig. 182, if the reversal takes 
place far enough before dead center for the centrifugal force of the rod 
end to have a considerable vertical component, the pin will roll in the 



§ 34 (c)] 



PRESSURES ON PINS AND BEARINGS- 



331 



bearing while changing from side to side, not jump across the clearance 
gap; this seems to be about the only advantage in having the reversal 
come early. 

In engines with a uniform rotary load, the exact timing of the force 
reversal is comparatively unimportant; but where the load is on the 
piston rod, as in pumping and blowing engines, it is well to have the 
development of forward driving force coincide in time with the develop- 
ment of resistance upon the working piston. Variation in the "lead" 
of the valve, or in the exact time of admission, is the important element 
of control in this connection. 



15^ 




Fig. 185. — Diagram of Guide Reaction. 



(d) Guide-bar Pressures. — The curves in Fig. 185, on a stroke- 
line base, show how the guide reaction Qg, in Figs. 153, 174, and 181, 
varies throughout both strokes: the ordinate from the base line to the 
curve represents the pressure of guide on crosshead. The full-line curve 
is gotten with exact rod inertia — see Fig. 154 for the general idea, but 
the method is not given in this book. The dotted curve shows Qg as 
complementary to S, in Fig. 174; and both are for values of Pd from 
Fig. 172. The true inertia effect of the rod tends to throw the wrist- 
pin end outward from the stroke line, having the same general direc- 
tion as the centrifugal tendency at the crank-pin end; the result is a 
lift during the forward stroke (decreasing Qg) and a down-pull during 
the return stroke (increasing Qg) ■ 

(e) Pressures on the Shaft Bearings. — The method of § 30 (e) 
and Fig. 155 III gives an entirely satisfactory solution to the problem 
of finding the pressures on the main bearings of an engine: but as 
there presented it is applicable only to the simple case where all 
the force actions are symmetrical with respect to the plane of mo- 
tion of the crank — that is, to a center-crank engine with equal 
wheels and with the same load forces on both wheels. The more 
general case of the ordinary side-crank engine is partly illustrated in 
Fig. 186. 

Considering only the effective driving force P as acting upon the 
crank pin, this force is held in equilibrium by the two bearing pressures 
Bi and B 2 ; the important dimensions being the overhang c of the crank 
pin beyond the middle of the main bearing Oi, and distance b between 



332 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



the latter and the outboard bearing 2 . Taking the origin of moments 
at 2 , we get Bi by the relation 



B 1 = b -±£ P . 



(192) 



and since Bi is the middle one of a set of three parallel forces, B 2 is 
equal to (Bi — P): or, taking moments about Oi, 



B 2 = tP. 



(193) 



Fig. 187 shows an extreme case of this extra pressure on the bearings; 
it is in correct proportions for a heavy locomotive, with long bearings 





a._ 



Fig. 186. — Bearing Pressures in a Side- Fig. 187. — The Main Driving Axle of a 
crank Engine. Locomotive. 

— necessarily kept within a definite limit of overall distance — and 
with the connecting rods outside the coupling rods. When, as here, 
the two forces Pi and P 2 are opposite in direction, they act together in 
producing a turning moment which can be balanced only by much 
larger bearing pressures Bi and B 2 . In the portions of the revolution 
during which Pi and P 2 point in the same direction, the B's are nearly 
equal to them. 

(/) Diagrams of Bearing Pressure. — To illustrate the applica- 
tion of Fig. 155 III, as modified by the conclusions in Art. (e), we 
apply the force actions represented in Figs. 172, 182, etc., to the engine 
shaft outlined in Fig. 188, belonging to a side-crank engine with the 
armature generator mounted beside the wheel. The load being in the 






§ 34 (/)] PRESSURES ON PINS AND BEARINGS. 333 

form of a torque only, if the armature is properly centered in the field, 
the forces to be combined are the crank-pin pressure P, the free counter- 
force Fb and the weight W. With the dimensions on the figure, these 
forces are divided between the bearings in the following proportions: 
Force at Oi at 2 

P H = L24 i| = 0.24(-) 

Fb 11 = 1.17 H = 0.17(-) 

W 11 = 0.59 11 = 0.41 

These ratios are got by the method of Eq. (192). 




Fig. 188. — Outline of Engine Shaft. 

In Fig. 189 is shown a series of force polygons like Fig. 155 III, taken 
at equal intervals around the crank circle, and determining the pressure 
Si at the main bearing of Fig. 188. These diagrams, like all the others, 




Fig. 189. — Pressures on the Main Bearing. 

show force per square inch of piston. The weight, W/A, is about 
15 lb., of which 9 lb. are carried at Oi, and 6 lb. at 2 ; Fb/A is 17 lb., 
equivalent to 17 X 1.17 = 20 lb. at d; while P is taken from Fig. 182 



334 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

and ^multiplied by 1.24. The resultants give Bi, in the direction of 
action of shaft on bearing. It will be noted that the pressure on the 
crank pin is decidedly the predominating force, and that the prevailing 
direction of bearing pressure is nearly along, the stroke line of the 
engine. 

Similar diagrams can easily be drawn for the outboard bearing, 
keeping in mind the reversed directions of the components of P and 
F B at 2 . 

§ 35. Balancing the Engine 

(a) Forces and Masses Involved. — As brought out in § 30 (/) 
and (g), the variable resultant of the inertia forces of all the moving 
parts of the engine is the force which tends to " shake" the body and 
foundation of the machine. Fig. 190 shows the masses and forces in- 




Fig. 190. — Accelerated Masses. 

volved in the problem of balancing, or of reducing the resultant free 
force to the least attainable value. The masses are 



Mi = total reciprocating mass, including part of the rod. 

M 2 = mass at crank pin, which may include, besides the rest of the 

rod, the crank pin and the crank arm or hub. 
Mz = mass of counterbalance, here taken at the radius OB, which 

is not necessarily the same as OC or R. 

The proper way to divide the mass of the rod has been described in 
§ 32 (a) ; the parts at the pins are made of such size as to keep the center 
of mass unchanged. With this division, there is exact equivalence to 
the real inertia force of the rod in amount and direction, but not quite 
the same line of action, since the resultant of the two partial forces 
must pass through the shaft axis. The proof of this statement is 
simple when the inertia action of the rod has been fully worked out, 
but in the absence of that analysis cannot be given here. 



§ 35 (a)] 



BALANCING THE ENGINE. 



335 



The slide inertia F\ is a component of F , the ideal centrifugal force 
of Mi according to Eq. (172), or 



Fi = F [ cos a + j cos 2 a 



)■ 



As to F 2 and F 3 , their resultant Fb = ^3 — F 2 (see Fig. 157) is the 
free counterforce whose horizontal component partly balances F\. 
This component is 

H = Fb cos a. 



By subtraction, we get the horizontal shaking force to be 
Sn = (F — Fb) cos a + j F cos 2 a. . . . 

The vertical shaking force is, very simply, 

Sv = — ^Bsina 



(194) 



(195) 



(6) Diagrams of Shaking Force. — A circular diagram which 
will give $h for any crank angle is derived from Fig. 168 by changing 




Fig. 191. — Shaking-force Components. 

the radius of the circle to (F — Fb) without changing the distance of 
points on the curve EiE 2 from the line GH. Thus, in Fig. 191 I, the 
diagram on AB is drawn with F as radius, and gives F\\ which would 
be identical with >Sh if M3 were made equivalent to Mi, or F 3 equal to 
F 2 — that is, if the rotating masses on the crank were brought to a 



336 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



perfect balance. If F3 were absent, Fb would be a negative quantity, 
and we should use the radius OAi = ^ + Fb: with this circle No. 1, 
the E-curve is stretched out vertically to EiE Ei. Diagram No. 2 is 
drawn for i^B = \ F and the E-curve is now squeezed together. 

The amount of counterweight necessary to bring the crank disc, 
with its attached rotating mass (part of the connecting rod), to a state 
of centrifugal balance about is well called the dead counterbalance: 
and the excess of F 3 over F 2 is then the free counterforce. 

Similar diagrams for the vertical shaking force $v*are given at II 
and III. In the first, for no counterweight at all, the minus sign is 
neutralized by that of Fb, and the angle scale has its zero point A at the 
left, as usual: but where Fb has a positive value, we must measure a 
from the other dead center in order to get Sy, in direction as well as 
intensity, by direct measurement from the figure. 




Fig. 192. — Shaking-force Curves. 

Diagrams on the developed crank circle are shown in Fig. 192. 
Here the first term of Eq. (194), (F — Fb) cos a, is laid off from the 
base PQP in one direction, in a simple sine curve for each value of 

(F — Fb); and the second term, y F cos 2a, is measured from PQP in 

Li 

the opposite direction, in a sine curve of half the principal period. 
Then Sr is given by the ordinate measured from this E-curve to the 
particular AB-curve, as indicated by the arrowheads. It is made 
apparent that with a high degree of balancing — with Fb a large fraction 
of F — the effect of the connecting rod, as shown by curve E E, be- 
comes of greater relative importance. 



§ 35 (c)] 



BALANCING THE ENGINE. 



337 



(c) The Side-ckank Duplex Engine. — The only engine truly 
represented by Fig. 190 is that with the center-crank arrangement, 
where the counterweights on the two cranks are symmetrical, so that 
they are equivalent to a single mass right in the axial plane. With the 
counterweight in another plane, relations exist analogous to those 
shown in Fig. 186. As covering this condition, and as a basis for the 
development of methods applicable to all multiple-unit engines, the 
mechanism of the common two-cylinder locomotive will now be con- 
sidered. On the outline, in Fig. 193, only the free or active counter- 




Fig. 193. — Inertia-force Outline of the Duplex Quarter-crank Engine. 

balance is shown. The problem is to get a combined effect of the slide 
inertias F\ and F 2 , and then test the balancing value of F s and F*, tak- 
ing account of the offset of the latter from the engine stroke lines. 

Viewing the plan of the engine at II, we see that none of these 
forces act through (or in the vertical plane of) the center of mass, 
which presumably lies in the plane projected in the line MN. Then 
according to the principle illustrated in Fig. 155, each of them, as F h 
will have two tendencies: first, to give the center of the whole engine 
mass a direct acceleration, as though the forces were along the line MN 
or in the vertical central plane, producing what we will call a shifting 
motion, second, to give an angular acceleration about a vertical axis 
through the center of mass, exerting the moment F x a and producing an 
oscillating motion. 

To get the combined shifting tendency of the two slide forces, we 



338 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



imagine them to be transferred to the central plane, taking their alge- 
braic sum as laid out at I in Fig. 193. Considering OCi, at the right- 
hand side of the machine, as the principal or leading crank, whose 
angle ai determines the position of the mechanism, and taking the 
inertia force to be positive toward the left, we have 



cos «i + y cos 2 ai 



Fi = Fo 

F 2 = Fo [cos («i - 90) + ^ cos (2 a x - 180)1 



= Fo ( sin a\ — y cos 2 an 



(196) 



(197) 



Adding these and dropping the subscript from a h we get, for the total 

f ° rCe ' Sn = Fo (cos a + sin a), ...... (198) 

the two rod effects neutralizing each other. 

(d) Graphical Determination of Shifting Force. — Now just as 
the principal part of F\ and of F 2 — respectively F cos a\ and F cos a 2 
— is the horizontal component of an ideal radial force, so also is the 
sum of these two, F (cos a + sin a), the horizontal component of a 
single radial force, which force is the resultant of the two F 's. This is 
proven in Fig. 194, where OCi and OC 2 are the respective F 's, and OC 
is their resultant: then DOCi is a, and 

ODi = F cos a, OD 2 = Fo sin a; 

also 

ODj = C 2 F = D 2 D: 

wherefore 

OD = Fo (cos a + sin a) = $h; 

and OD is the horizontal component of OC. This OC is V2 X ^o or 
1.414 Fo, and the value of Sr is therefore 

Sr= 1.414 Fo cos (a - 45°). . (199) 

The two counterforces, shifted to 
the center plane and represented by 
OBx and OB 2 in Fig. 194 II, can like- 
wise be replaced by a single resultant 
OB, whose horizontal component OE 
will oppose OD, while the vertical 
component EB will be a free shaking 
force. 
The results of this investigation are expressed in complete graphical 
form by Fig. 195. The circle in I is drawn with 1.414 (Fo — Fb) as 
radius, Fb standing for either F$ or F 4 on Fig. 193. The zero of the 




Fig. 194. — Combined Radial Effects. 






§ 35 (d)] 



BALANCING THE ENGINE. 



339 



angle scale is located at the position which OC, Fig. 194, will occupy 
when a for crank No. 1 is zero, or when OCi is on its zero dead center: 
and to get Sr we locate the actual value of a on this angle scale and 
measure over from the circle to GH. 




270 C 



II. 


1, 





ZJS/ 


T 


^"Xoo 






1 




III. 




■r 






Jz 


A ( 












1 


/I 


< 











1 


/ 
/ 
/ 

/ 












1 1 






c 2 




180 










9 



H 



Fig. 195. — Diagrams of Shifting Force. 



In Fig. 195 II, the diminution of OCi and OC 2 by dJi and C2J2, 
each equal to Fb, is shown with the purpose of giving a clear idea of 
the size of the primary forces. Then the resultant OK is the radius in 
I; while CK, the same as OB in Fig. 194 II, is used as radius in III. 
This second circle shows the vertical shaking force Sv in the same way 
that I gives Sb.: its zero of angle is diametrically opposite to that in I, 
and the forces are measured vertically from AB. 

(e) Torque Effect of the Combined Inertias. — Referring to 
Fig. 193 II, we note that F x and F 2 both act at the end of the lever 
arm a; and that when they point in the same absolute direction their 
moments oppose each other. The 
best way to combine them is to im- 
agine F 2 to be swung, at the end of 
its radius a, through 180 deg. about 
some point on MN, until it comes 
into the line of Fi : then the algebraic 
sum of the two forces in this position 
— which is the same as their alge- 
braic difference with F 2 in its actual 
direction — is a resultant free force 
acting at the end of the radius a to 
give the engine an angular accelera- 
tion about a vertical axis through the 
center of mass. Calling this turning or twisting force Tu, we have, with- 
out counterbalance, from Eqs. (196) and (197), 

Tn = F l -F 2 = F Q (cos a 

the two rod effects acting together in this combination. 




Fig. 196. — Radial Twisting Effects. 



sin a) -\-2jFq cos 2 a, 



(200) 



340 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

In Fig. 196, the reversal of F 2 in bringing it into the line of Fi is 
represented by the reversal of the F for the left side, from OC 2 to OC3 : 

then the major part of the force Tb. is the horizontal component of OC: 
for 

OD = ODi - DDx = OB 1 - D 3 = F (cos a - sin a). 

The two counterforces are combined in the same way at II, after 
reversing that for the left side, just as in Fig. 194 II: except that a 
reduced value of F 3 and F 4 , or of Fb, must be used. That is, Fb at the 
radius b will be represented by a smaller force Fb' at the radius a, ac- 
cording to the equation 

F B b = F B 'a, 
or 

Fb' = -F b . (201) 

a 

This reduced force is laid off as OBi and OB 2 in II, b/a having the 
value 0.8. 

To give the harmonic-motion component of the net inertia torque, 
a circular diagram like Fig. 195 I would have the radius 1.414 (F — Fb') 
and its zero at 45 deg. above OA. The rod-effect component might be 
got from a diagram similar to the curve EE E in Fig. 191, but a simpler 
method for that force is developed in the next article. 

Considering possible oscillation about the three principal axes 
through the center of mass of a locomotive, the conditions as to plane 
of motion, axis of rotation, and turning force may be summarized as 
follows : 

In horizontal plane, about vertical axis, net force Tr with moment 
arm a; 

In vertical cross plane, about longitudinal axis, vertical component 
of OB, Fig. 196, with moment arm a; 

In vertical longitudinal plane, about horizontal cross axis, net Sn 
(from Fig. 195 I) with distance from center of mass down to a plane 
through the two engine axes as moment arm. 

In representing these moments each by a single force at the end of 
a lever arm from the center of mass, there must be the underlying idea 
of an equal and opposite inertia force (actual or equivalent), of the body 
mass at the center, which serves as the other force of a " couple." 

(/) Determination of the Rod Effect. — The circular diagram 
as in Fig. 195 gives in very simple fashion the harmonic-motion or 
F cos a portion of the slide inertia. From the expression 

/ = ? F cos 2 a = nF cos 2 a, (202) 



§ 35 (/)] 



BALANCING THE ENGINE. 



341 



for the component due to modification of slide motion by the connect- 
ing rod, an equally easy and general way of getting the resultant of 
several rod effects is derived in Fig. 197. At I, F Q has the usual mean- 
ing, while /o is a similar ideal radial centrifugal force of the value 
/o = nFo, so that Eq. (202) becomes 



/ = /o cos 2 a. 



(203) 



The form of this equation suggests that /, being a sine function, can be 
shown by a plain circular diagram of the type that gives F = F cos a 



F a * 



J&3 




90 c 




<— 




Fig. 197. — Circular Diagram of Rod Effect. 



so readily; but it appears that the determining point on the circle, or 
the radius /o, will have to rotate twice as fast as the crank. In illus- 
tration, five positions of the radial forces are shown, with / making a 
complete revolution while F turns through 180 deg. At deg., / is 
moved off to one side of F , with which it really coincides, for distinct- 
ness of representation. The circle in II is drawn with / , enlarged, as 
radius: and the use of the double angle scale, going twice around the 
circle, is self-evident. When the crank is at any angle a, the end of 
/o is at the correspondingly numbered 
point on the scale: and the distance to 
the vertical diameter is /. 

(g) The Method of the Radial 
Resultant is made complete by the 
expedient just devised, the application 
of which to the locomotive or quarter- 
crank engine is illustrated by Fig. 198. 
First, at I, the radial forces are laid out 
as if the two cranks were together at the Fig. 198. - - Rod Effect in the Quar- 
zero dead center. When crank No. 2 

is turned back through 90 deg. in order to get the actual arrangement, 
at II, / 20 turns twice as far as F 2 o, so that the rod effects oppose and 
neutralize each other in shifting tendency. But when, for torque effect, 



*~r 


-Jk 


1 
1 


III. 




*20 C 


J ZQ 


/ 


■V * 




} 

J zo 


II. 


V 


~~JZQ 



1 




342 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

we reverse F 20 by the device of swinging it bodily into the plane of F w , 
we likewise reverse /20; and then, as shown at III, the rod effects com- 
bine. Of course, the radial resultant of the two F 's will be used, as in 
Fig. 195. 

Another example is given in Fig. 199: in rotating F 2 o through 180 deg., 
from the common position shown in Fig. 198 I, we turn / 20 through 
360 deg.; then the main components are self-balanced, and only the 
double rod effect is active for direct acceleration. Reversing F 2 o, at II, 
we see that the slide inertias act together to produce angular shake; so 
that unless the cylinders are so close together as to give a very short 

lever arm for the couple, counterbal- 
"**2° ancing may be necessary. The rod 
effects, however, neutralize each other 
in this action. 

In comparison with the trigono- 
metrical method of Eqs. (198) and 
(200), this has the advantage of avoid- 
ing complicated formulas when the an- 

Fig. 199. — Radial Analysis of the gl es between the cranks are not quad- 
Engine with Two Cranks at 180 deg. . (-.I • j lT_' j l ,1 1 /• 

rants; lurtner, it obviates the need of 
interpreting the direction meaning of the algebraic sign of the angle 
functions, which is likely to be mentally confusing. It must be clearly 
understood that the radial resultants are imaginary, as are the F 's and 
/o's from which they are derived; only the components along the axis or 
stroke line of the engine are real forces. Lack of space forbids the 
further exposition of this scheme, but it is very effective for determining 
the resultant influence of the inertia forces of the moving parts in the 
more complex engines. Generally, such engines are largely self-bal- 
anced, so that there is little need to place counter weights on the 
cranks. In any case, the final result is best shown by developed dia- 
grams similar to Fig. 192. With either type of two-crank engine, 
for instance, there will be three curves, one from each F and Fb result- 
ant (as from circles I and III in Fig. 195) and one from the resultant of 
the /o's. As the reciprocating masses more nearly balance each other, 
the relative magnitude of the rod effect increases. 

(h) Effects of the Shaking Force. — It is far easier to deter- 
mine the unbalanced inertia force of the moving parts of an engine 
than to predict what effect this force will have in producing undesired 
motion of the machine as a whole: in fact, an answer to this latter 
question can be given only in general terms. 

If the engine was supported in such a way that it could move 
freely in any direction, the recoil of the moving parts would give to it 



! 



§ 35 (h)] BALANCING THE ENGINE. 343 

a motion similar to that of these internally-moving bodies, but smaller 
in the inverse ratio of the masses. By greatly increasing the " fixed" 
mass, or by bolting the engine to a heavy foundation, the amplitude of 
this motion is made very small. With earth-borne foundations, the 
shaking effect may be a mere tremor, hardly perceptible, a great deal 
depending upon the character and structure of the earth or rock upon 
which the foundation rests. 

With a more elastic support, as in a ship or, occasionally, on the 
floor of a building, a large part of the structure will take up the motion 
of the engine bed, and the highest attainable degree of internal balanc- 
ing becomes desirable. The worst disturbance is produced when the 
period of variation of the shaking force coincides with that of the elastic 
vibration of the structure. The latter is something that can be found 
only by trial. 

In the preceding discussion of the combined effects in a complex 
engine, it is assumed that the engine is so compact and rigid that the 
several forces can be truly represented, as to their external effect, by a 
single resultant. Where the several parts are connected only by the 
foundations, as in many stationary engines of the "spread-out" type of 
construction, the separate force actions in the respective single engines 
are of greater interest than the combined effect. But engines in which 
the inertia forces are large — high-speed engines of any class — are 
usually of the close-constructed, self-contained type. 

§ 36. Construction of the Engine. 

(a) The Cylinder. — So far as the function of containing steam 
is concerned, the cylinder need be nothing more than a plain shell with 
heads bolted to the flanges, as it appears in the simple sectional view in 
"Fig. 2. To provide for handling the steam, the valve chamber and 
steam passages must be added, greatly complicating the casting. A 
third requirement is the suitable support and holding of the cylinder, 
against its own weight and against the far greater working forces due 
to steam pressure. 

Body of the Cylinder. — The main part of the inside surface, along 
which the piston slides, is called the bore of the cylinder; at the ends it 
is counterbored a little larger (from § in. to \ in. on the diameter). 
This is done partly to facilitate reboring when worn, partly in order 
that the piston may not wear the rubbing surface to a shoulder at the 
end of its stroke: with the latter intent, the outer edge of the packing 
ring is even made to travel a little beyond the end of the bore in an 
engine like Fig. 200. The cylinder heads project into the counterbore, 



344 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 




Fig. 200. — Lengthwise Section of Locomotive Cylinder, with short, wide, balanced 
slide valve and long ports. Scale 1 to 12. 



1. Cylinder body or barrel. 

2. Cylinder flanges. 

3. Front cylinder head. 

4. Back cylinder head. 

5. Stuffing box. 

6. Piston. 

7. Piston rod. 

8. Packing rings. 

9. Steam ports. 
10. Exhaust port. 



""mil ^ 






/ H, 




» 


1 J! 

© 2- 
1 


. mill inn ) 




>nr 








k, JU> 



11. Valve seat. 

12. Steam-inlet ports. 

13. Valve-chest base. 

17, 18. Stiffening strutts across ports. 

19. Drain-cock taps. 

21. Valve-chest body. 

22. Valve-chest cover. 

23. Balance plate. 

24. Valve. 

25. Valve yoke and rod. 



R 



Fig. 201. — Top View of Valve and Yoke in Fig. 200. 1, 2, Balance strips. 



§ 36 (a)] 



CONSTRUCTION OF THE ENGINE. 



345 



are conformed to the surface of the piston, and are stiffened by radial 
ribs on the outside. Fig. 200 shows them shallow, Fig. 203 very deep. 
We distinguish the full or plain outer head (at the head end) and the 
inner or stuffing-box head (at the crank end). In Fig. 203, with an 
extended piston rod, both heads contain stuffing boxes: here the heads 
are steam-jacketed, as well as the cylinder body, and the front head is 
cast with the cylinder. In the latter arrangement, it is the regular 




Fig. 202. — Cylinder of 15 in. by 14 in. High-speed Engine in Fig. 2, showing 
double-seated flat valve. Scale 1 to 14. 



thing to make an opening large enough for the passage of a heavy bor- 
ing bar, then close it by a bushing or small head which carries the stuffing 
box. Fig. 200 shows distinctly the narrow contact surface of the 
ground joint between head and cylinder; by concentrating the pressure 
due to the bolts on this narrow, accurately-finished ring surface, tight- 
ness is secured without the use of any packing. With plain flange faces, 
a gasket is commonly used, of heavy paper or very thin sheet packing, 
or of soft metal. 



346 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 







Fig. 203. — Lift-valve Engine, German Design; high-pressure cylinder of 670 and 
1075 by 1200 mm. compound engine, with full steam jackets. Scale about 1 to 
30. 



§ 36 (a)] CONSTRUCTION OF THE ENGINE. 347 

Formation of Steam Jacket. — In Fig. 203 is shown a jacket space 
cored in the main casting, a very common method of construction, 
especially in small and moderate sizes. To simplify the work of the 
foundry,, both as to form of mold and in making it easier to get a sound 
casting, the steam jacket is often shut off by means of a separate inner 
shell or liner. This renders possible the use of a particularly hard and 
dense metal for the rubbing surface; but it adds joints which must.be 
made and kept steam-tight. 

Valve Chest and Steam Passages. — Fig. 200 shows an extreme type 
of the single slide-valve arrangement, the valve being short and the 
ports long; the valve chest is a separate box casting, and the joints 
between it and the cylinder and the cover are made tight by a copper- 
wire gasket; the valve detail in Fig. 201 will be referred to from the 
next chapter. In Figs. 9 and 259 we see the long slide valve, with 
short ports, and have representative examples of the two forms of 
balanced valve. Fig. 202 illustrates the cutting back of the ports into 
the cylinder-head space, as is markedly done in Fig. 203 also: the 
double-faced balanced valve is an excellent form, but requires rather 
long ports. Figs. 203 and 265 show four separate single-function valves, 
placed at the four " corners" of the cylinder. 

The matter of valve form and action is taken up in the next chapter. 
Here it may be noted that the single slide valve, controlling two ad- 
missions and two exhausts (that is, the whole steam distribution at 
both ends) is properly called a four-function valve. Sometimes an 
engine will have one slide valve for admission and one for exhaust, each 
a two-function valve. The complete separation of function, as in 
Figs. 203 and 265, has many advantages in large engines, making the 
valve chambers smaller, simplifying the ports, and giving greater flexi- 
bility in the control of steam action. 

Support of the Cylinder. — In the small high-speed, short-stroke 
engine, like Fig. 2, a single cylinder is bolted fast to the frame at the 
flange and allowed to overhang, its weight being relatively insignificant : 
if, however, the engine is a tandem compound, the outer cylinder is 
supported from the foundation. In vertical engines, this end support 
of the cylinder is all that is ever needed. Large horizontal engines 
have the cylinders resting on the foundation, as in Figs. 3, 203, and 
265, a suitable base or footing being formed on the cylinder casting. 
The locomotive, represented by Fig. 200, is the only engine of current 
type that has its cylinder wholly supported from the side. 

(b) Framework of the Engine. — The bed or body of the small, 
compact, high-speed engine is well represented by the example in Figs. 
2, 5, and 7; when a side-crank engine of this type has a separate outer 



348 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

bearing, or, in general, when the engine is direct-connected to a genera- 
tor, there is usually an iron sub-base which extends out beneath this 
bearing, so that the engine does not depend upon the masonry founda- 
tion for alignment. The slower-running Corliss (or equivalent) engine 
has such a large wheel that the outboard bearing must be supported on 
a separate pier, which rises from the main foundation. The lighter 
and more open form of frame for such machine is outlined in Fig. 1, 
while Fig. 204 shows, to larger scale and in considerable detail, the 




4J2&P 



Fig. 204. — Frame of 26 in. by 48 in. Corliss Engine in Fig. 3. Scale 1 to 60. 



frame casting of the modern, heavy-duty Corliss engine described in 
Chapter I; this is of the hollow, box form, with enclosed guides, and 
has a full-length bearing upon the foundation. 

(c) The Piston. — Sectional views of the plain, hollow cast-iron 
box piston are given in Figs. 200, 202, 203, and 259: this is overwhelm- 
ingly prevalent for diameters up to 24 in., and is used up to as much as 
48 in. Radial ribs are generally put in to stiffen the casting. In width 
of face or thickness of piston, Figs. 200 and 202 show extreme cases. 
Usually there are two plain packing rings, set near the edges of the face. 

A number of single-disc pistons are given in Fig. 205. The cone 
disc at III represents the type mostly used in marine engines. The 
design at IV is special in having a cast-iron face ring on a cast-steel 
body: this gives a rather better surface as regards wear of the cylinder, 
and the ring is made broader at the bottom over 120 deg. of circum- 
ference, giving it more weight-carrying surface. An advantage of this 
arrangement is that when the cylinder is rebored only the face ring, 



§ 36 (c)] 



CONSTRUCTION OF THE ENGINE. 



349 



not the whole piston, need be renewed. With all these pistons, the 
inner face of the cylinder head (or heads) is made to conform closely 





Fig. 205. — Locomotive Pistons of the Solid-disc Type. Scale 1 to 12. 

to the shape of the piston surface, and thus keep down the clearance 
volume. 

In Corliss engines, the built-up piston is usual, exemplified in Fig. 
206. There is first the ribbed body or spider, fast on the rod. The 




Fig. 206. — Piston for Corliss Engine in Fig. 3. Scale 1 to 12. 
1. Body or "spider." 2. Bull ring. 3. Follower plate. 

v 

face or rim is formed by the bull ring, which can be adjusted on the 
body by set screws so as to get the piston rod into a truly axial position 
and keep it there as against wear of the sliding surfaces. Finally, the 
piston is closed by a follower plate, held in place by tap bolts. 



350 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

(d) Piston Packing. — The plain solid or one-piece, self-elastic 
packing ring, called a snap ring, is used in all small pistons and many 
large ones. Commonly of hard cast iron (sometimes of steel), this is 
turned to a diameter a little larger than the cylinder bore, then a piece 
is cut out of such length that when the piston is shoved into the cylinder 
the ends will just come together: a refinement of construction is to 
press the ends together, clamp the ring between two discs on a mandrel, 
and with a fine cut make it truly cylindrical when thus bent to the 
working diameter. Very often the ring is of uniform thickness; but it 
is better, especially with large diameters, to turn the inner surface 
slightly eccentric with the outer and make the cut on the thin side, 
thus getting a taper toward the joint. Very often the ends meet in a 
plain butt joint, but some form of lap is preferable because more effec- 
tive to prevent leakage: in a horizontal engine the ring joints are 
usually kept at the bottom of the piston, but in a vertical cylinder the 
joints are placed opposite or far apart. 

In Fig. 206 the one ring is in eight segments, which are pushed out 
by little coiled springs under the joint pieces. Such segmental rings 
are much used in large pistons, and are made in a great variety of 
forms. Occasionally auxiliary springs are used beneath one-piece 
rings. 

(e) The Piston Rod. — The type of joint at piston and at cross- 
head is the chief point of interest in connection with this piece. The 
cone fit and nut, Figs. 2, 200, 203, etc., is most common at the piston: 
a straight fit is shown in Fig. 205 III, screw threads in the piston in 
Figs. 205 II and 259. With a very long taper, say from 1 in 20 to 1 in 
40, it is important that the piston be brought up against a shoulder, to 
limit the wedge action of the rod; this shoulder may be formed by a 
reduction of diameter, as in Fig. 206, but it is better to have a collar on 
the rod, as in Fig. 200 or Fig. 205 IV. 

At the crosshead, the screw and jam-nut joint seen in Figs. 2, 208, 
209, and 210 is. almost universal; except that in the locomotive the 
cotter shown by Fig. 211 is regularly used. 

(/) Piston-rod Packing. — For use in stuffing boxes, around 
piston and valve rods, soft or fibrous packing was long the only ma- 
terial employed; and it is only under more severe conditions of service 
and pressure that metallic packing has been coming into general use. 
Soft packings are made of vegetable fiber (hemp, etc.), asbestos, and 
rubber, in various combinations, with graphite frequently incorporated 
as a lubricant: there is on the market a host of these, ready-made in 
uniform and graded sizes, so as to fit and fill neatly the annular space 
around the rod. 



§ 36 (/)] 



CONSTRUCTION OF THE ENGINE. 



351 



As to the stuffing box, we note that the end surfaces may be either 
flat as in Fig. 9 or conical as in Fig. 265. To allow for initial or ac- 
quired faults in alignment and for wear of the sliding surfaces of piston 
and crosshead, the rod must fit but loosely where it passes through the 
cylinder head and the gland. Quite often bushings of brass or linings 
of babbitt metal are used, as seen in Figs. 2 and 203. 

A typical metallic packing is shown in Fig. 207. The gland G is 
here a mere heavy cover plate, made tight by a copper-wire ring 
basket. The ball ring 1 is seated upon the gland with a spherical 




Fig. 207. — Metallic Piston-rod Packing, to fit stuffing box in Fig. 200. 



ground joint; the casing 2 is free to move side wise, and contains the 
three babbitt-metal packing rings 3, 4, 5, which are the only parts that 
touch the rod. These, as pieces requiring comparatively frequent re- 
newal, are made in segments so that they can be put in without dis- 
turbing the rod connections, and are placed in the cup so as to " break 
joints.'' The follower 6 is pushed up by the spring, which is itself 
held in the light casing 7. This spring is not expected to do much more 
than hold the rings in place : it is the steam pressure that wedges the 
rings into the cup and makes the joint tight, so that the tightness of the 
joint varies with the pressure of the steam to be held. 

The same packing, with different proportions, is shown in detail at 
C — the difference consisting in the slant of the confining surfaces of 
the cup, which causes all the rings to come into action, although the 
first one still takes most of the wear. And at D is given the detail of 
another packing of this same wedge-action type, with brass rubbing 
rings. 

(g) The Crosshead. — The three typical forms of this piece are, 
four-bar or wing crosshead of Fig. 208, the slipper type in Fig. 209, 
and the block or trunk form in Figs. 210 and 211. The first requires 
four guide bars, two at each side, and is little used; the second has but 






352 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

one main surface, although top bars extend inward over the edges of 
the flat soleplate, to prevent lifting of the crosshead; the third form, 




Fig. 208. — Crosshead from Engine in Fig. 2, of four-bar type. View D shows 
grooves in bottom face which are filled with babbitt metal, so that rubbing 
surface is partly babbitt, partly cast iron: view E shows how wrist pin is lubri- 
cated by oil caught from guides. Scale 1 to 10. 




Fig. 209. — Crosshead of Slipper Type, with cast-steel body and cast-iron soleplate; 

hollow cast-iron wrist pin. 

with guides below and above in the plane of the mechanism, is the most 
used. 

In general, any crosshead has the two functions of joining the con- 
necting rod to the piston rod and of sliding upon or between the guides : 



§ 36 (g)] 



CONSTRUCTION OF THE ENGINE. 



353 




Fig. 210. — Crosshead of Block Type, for bored or cylindrical guides, as in Fig. 6, 
and with adjustable wedge shoes. View E shows inside of shoe, with holes for 
cap screws; view F shows dovetail grooves for holding babbitt facing. 




f € gyp 3 




Fig. 211. — Block Crosshead of the "Alligator" Form, commonly used in locomo- 
tives; this to accompany cylinder in Fig. 200. Body and shoes of cast steel; 
rubbing surfaces faced with tin, which is self -soldered to steel. Scale 1 to 12. 



354 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

it consists therefore of the body, which begins with the hub for the 
piston rod and is usually forked to receive the wrist pin, together with 
the sliding faces or shoes, of whatever form. As to the wrist pin, 
cylindrical fits are shown in Figs. 208 and 209, taper fits in the other 
two examples. In Fig. 208 the pin is driven in tight and the rod has a 
strap end; usually, however, the wrist pin is made easily removable 
and this is essential with a solid-end rod. The figures show different 
kinds of rubbing surface, but only the one example in Fig. 210 (char- 
acteristic of large, stationary engines) has provision for adjustment to 
take up wear. 

(h) The Connecting Rod. — This piece may be analyzed into a 
shank or body and two ends or heads. In large, slow-running engines 
the shank is usually round, largest in the middle and tapering toward 
the heads, as in Fig. 212; at higher speeds this type changes to one long 
cone, tapering outward toward the crank end and flatted on the sides so 




Fig. 212. — Connecting Rod with Solid Ends, belonging to Corliss engine in Fig. 

3. Scale 1 to 15. 



that it approaches a rectangular section as the diameter increases. 
Stationary high-speed engines (Fig. 2) and many locomotives have the 
rectangular section, increasing in depth toward the crank end. For 
fast locomotives the sides of the bar are milled out, giving the I-beam 
section in Fig. 214. These differences are dictated by the need of pro- 
viding resistance to the transverse inertia forces which result from 
the swing of the rod. In stationary engines, the ratio of rod length to 
crank radius is commonly 6, or somewhere near that value; in locomo- 
tives it ranges from 6 to 10, and in marine engines is usually about 4. 

At each end of the rod there is an adjustable bearing for one of the 
pins. The " boxes " or " brasses " which form the bearing proper 
mast be enclosed in a frame or casing of suitable form and strength, 
and provision must be made for setting them to a proper fit upon the 



§ 36 (h)] 



CONSTRUCTION OF THE ENGINE. 



355 



pin and for taking up wear. Four types of rod end may be here differ- 
entiated: the solid end is simplest in construction, but it cannot be used 
with an inside crank, and the boxes have a minimum of holding flange 
on one side, as appears in views C and D of Fig. 213. The bolted 





rrprrprnnrrn . 




dJjiLJJiiJJ^ 



Fig. 213. — Rod with Bolted Strap at Crank-pin end, for 22 and 42 by 27 in. cross- 
compound engine at 175 r.p.m. Scale 1 to 15. 

strap is a very good type of end construction, while the essentially equiv- 
alent jaw end in Fig. 214 is based on German practice. The marine 




4 






Fig. 214. — Rod for Locomotive, with special forked end. Scale 1 to 12. 

type, at the crank pin in Fig. 2, is used almost without exception on 
marine engines, and very largely in stationary practice. 

A point to be noted is whether adjustment for wear will shorten or 
lengthen the rod. In Figs. 2, 212, and 214 the two take-ups tend to 
balance each other, but in Fig. 213 the two work together to increase 
the length between centers. Except in the very severe locomotive 



356 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



service, crank-pin boxes are generally lined with white metal, being 
commonly made of cast iron or steel; at the smaller wrist pin, with 
much less motion in the joint, brass boxes are almost universal. 

(i) The Crank Shaft. — The usual type of shaft for stationary 
side-crank engines is well represented by Fig. 215 I. Shaft and crank 
pin are of mild steel, the disc is of cast iron with a fan-shaped counter- 
weight formed upon it. They are put together with either forced or 




Fig. 215. — Large Shafts with Built-up End Cranks. I, for engine in Fig. 3, scale 
1 to 40; II, for 44 and 88 by 60 in. duplex horizontal-vertical Corliss, like that 
in Fig. 137, rated 8000 i.h.p. at 75 r.p.m. Scale 1 to 72. 

shrunk fits, the holes in the disc being bored about one in one thou- 
sand smaller than the pieces which are to go into them. The crank 
pin is riveted over for greater security, and has a detachable cap, to 
receive the solid-end connecting rod shown in Fig. 212. To carry the 
weight of the wheel and generator, the shaft is enlarged between the 
bearings; but its diameter can be reduced where it enters the crank 
hub without sacrifice of needed strength, although the proportion of 
reduction is greater in this case than where the conditions of working 
are more severe. 

Figure 215 II shows the shaft for a large duplex horizontal- vertical 
engine. The straight shaft is a hollow forging of high-grade steel, oil- 
tempered; the discs or webs are massive steel castings. Referring to 



§ 36 (i)] 



CONSTRUCTION OF THE ENGINE. 



357 



the outline in Fig. 137, we see that the two connecting rods act upon 
one pin, as here indicated by the letters H and V. 

A typical shaft for a high-speed center-crank engine is shown in 
Figs. 2 and 7. To use a complete disc as in Fig. 215 I neutralizes a 
good deal of the off-center mass, and the fan-weight form is therefore 
more effective. Since the crank is enclosed, appearances do not suffer, 
and the connecting rod is more accessible than if shut in between cir- 
cular discs. When a greater counterforce is needed than can con- 
veniently be provided with iron, the " weights " are made hollow and 
filled with lead, especially on locomotive wheels. 

Beside large built-up arrangements as in Fig. 215, solid-forged 
shafts are much used in marine engines, more on naval vessels than 
in merchant service. 

(j) Bearings. — Fig. 216 shows a number of bearings from small 
high-speed engines. The arrangement at I is simple and very satis- 
factory as long as the bearing surface remains in good working order; 




Fig. 216. — Bearings for High-speed. Stationary Engines. I, one-piece bushing, 
with elastic adjustment; II, simple bearing in two parts; III, ring-oiling bearing 
in four parts. 



but the fact that a wheel must be taken off in order to replace a damaged 
bearing shell has led to the substitution of a two-piece bushing, with a 
solidly-bolted joint at the bottom. 

A very simple two-piece bearing is shown at II. The main set- 
screw adjustment is at the right, while that on top obviates the need of 
close fitting of the cap on the bearing boxes. With only a slight side- 
wise displacement of the shaft, the lower box can be easily taken out 



358 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 



for examination or repair. Beneath the main view is a detail of the 
universal key which fits into a round hole in the bed and a cross-slot in 
the bottom box, so as to hold the latter against endwise movement. 

At III in Fig. 216 a four-part bearing with oiling rings is drawn 
more in detail. The adjustable quarter box 5 is backed by a face 
block 2, of which the outer surface is cylindrical below the level of the 
shaft axis, so that it can be easily taken out. In view D are shown the 
holes for lifting screws which are tapped in the several parts of the 
bearings. In the middle of the bearing, at the top, is a screw pin 
which serves as a dowel, to keep the boxes from ever turning with the 
shaft. View C is a plan of the casing, with the boxes removed. The 
lubrication arrangements, besides the oil well and the rings with peep 
holes above them, include a light collar fastened upon the shaft at the 
outer end of the bearing, to catch all oil that escapes and return it to 
the well. At the inner end the oil drips upon the projection L, from 
which it is scraped by a little catcher on the crank disc, and carried to 
the crank pin. 




Fig. 217. — Bearings for Engines of the Corliss Type. I, from engine in Fig. 3, 
scale 1 to 24; II, III, different arrangements of adjusting wedges. 

Corliss-engine Bearings. — In horizontal engines of the Corliss type, 
the bearings are usually made in four parts, with side adjustment either 



§ 36 (A;)] 



CONSTRUCTION OF THE ENGINE. 



359 



by set screws or by wedges. Fig. 217 I shows vertical adjustment also, 
by means of the wedge drawn in detail at C. It is hardly possible that 
a lifting force greater than the weight of the shaft and wheel will ever 
be developed in an engine of this class; consequently, the top box is 
made light, and is held down simply by contact with the cap at the 
ends. The big hollow cap is characteristic. In view B, the upper half 
is a plan of the bearing cap, and the lower half is partly a top view of 
the base, partly a section by a plane through the shaft axis. 

Figure 217 II shows a double-wedge adjustment, the wedges being 
drawn up by long studs, with nuts on top of the cap. With this ar- 
rangement in only one of the two bearings, it is possible always to 
square the shaft with the stroke line, besides taking up wear — pro- 
vided the bottom box can move, as in this case. Where the lower part 
of the bearing is solid with the frame, as at III, the wedges can be used 




Fig. 218. — Fly-wheel Hubs for Small Engines. I, standard design; II, for engine 

in Fig. 2. Scale 1 to 16. 

only to adjust the side boxes to a proper fit. These wedges are raised 
by set screws, which go through them and rest upon the seatings 
beneath them, so that the cap can be taken off without affecting the 
adjustment. 

(k) Wheels. — The two typical forms of engine wheel are very 
well shown in Figs. 2 and 7 and in Fig. 3. Stationary engines for gen- 
eral service are made with wheels of the belt-pulley type, and in the 
smaller sizes this is commonly retained when the engines are direct-con- 
nected to generators'. For larger machines, direct-connected or di- 
rectly loaded, the balance-wheel type with rectangular cross section is 
usual. 

Small belt-pulley wheels are made with inside flanges on the rim, 
as in Fig. 7. With diameters less than 9 ft. they are usually cast in 
one piece; but very generally the hubs are split, on one side or all the 
way through, so that they can be clamped upon the shaft. Fig. 218 II 
is a typical arrangement, with two bolts at one side of the hub and a 
common rectangular key. At II there is a single big bolt in the plane 



360 WORKING AND CONSTRUCTION OF THE ENGINE. [Chap. VII. 

of the arms, and the key is replaced by set screws which fit into pockets 
milled in the shaft. 

Wheels up to 16 ft. in diameter are commonly made in halves — 
the size of the largest piece that can be shipped on an ordinary rail- 
road car having a good deal of influence in this matter. A representa- 
tive example of the balance-wheel type is detailed at I in Fig. 219. 




Fig. 219. — Balance Wheels of Medium Size. I, from engine in Fig. 3; diameter 
16 ft., weight 62,000 lb., scale 1 to 48; II to VI, details of wheel joints. 

The hub is strongly clamped upon the shaft by four heavy bolts, while 
the strongest part of the rim joint consists of the two I-shaped shrink 
bolts or links. Wheels of this size will be completely finished in the 
shop; and to insure a neat fit at the joints, little screw dowels are put 
into holes drilled and tapped half and half in the two parts. When the 
engine is erected, these will be inserted first, along with the light bolts 



§ 36 (k)) CONSTRUCTION OF THE ENGINE 361 

through the lugs on the inside of the rim: and the shrink bolts are put 
in last of all. 

Another form of connecting link is shown at II, the name " link " 
being here closely descriptive. At III a U-shaped tie is used along 
with I links. The tie bar with keys, Fig. 219 II, is sometimes used 
for low speeds and light stresses: this is not a shrunk joint, but is 
tightened by making the keys with a slight taper and driving them in 
hard. 

Large wheels of the belt-pulley type are generally joined by bolted 
flanges, after the manner of the sketch at V. In large diameters, 
wheels of either type are made in a number of segments, each with one 
or two arms, and the arms are held in a built-up hub. Belt wheels have 
been constructed with the arms separate from the rim segments and 
bolted fast as in Fig. 219 VI (the arms having a cross-shaped section) 
but it is better to cast rim and arms together. 



CHAPTER VIII 
VALVE GEARS AND GOVERNORS 

§ 37. The Simple Slide Valve, with Harmonic Motion 

(a) The General Form and manner of action of the slide valve 
and its driving gear are illustrated and explained in Chapter I. The 
first step in a closer study is to establish simple and convenient graphi- 
cal methods for showing the movement of the valve, or for readily 
finding its position corresponding to any position of the crank or 
piston. The movement of the valve is determined by the rotating 
eccentric, just as that of the engine piston is determined by the crank, 





Fig. 220. —The Valve Mechanism 
Reduced. 



Fig. 221. —The Reuleaux Diagram. 



and the deductions in § 31 apply equally to the valve gear. The pres- 
ent problem is simplified by the fact that the eccentric rod is usually so 
long, relative to the radius of the eccentric, that the valve receives 
practically harmonic motion: then, for kinematic study, the whole 
mechanism, including the main crank arm, may be reduced to the form 
shown in Fig. 220. 

This is a modification of Fig. 158; and by placing the slide beneath 
the eccentric circle we emphasize the fact that the distance of the valve 
from its mid-position, or MV, is the same as the distance SE of the 

362 



§ 37 (a)] SIMPLE SLIDE VALVE, WITH HARMONIC MOTION 363 



eccentric center E from the vertical center line SO. The position of 
the valve is denned by giving this distance, measured to the right or 
left: we shall call it the valve travel, and denote it by t. 

(b) Movement Diagrams. — In order to get the valve travel 
corresponding to any crank position, knowing the eccentric angle 8 or 
COE in Fig. 220, we must measure forward this angle 8 and find the 
length of ES or t. But a truly serviceable diagram should give t di- 
rectly from the crank angle, without the bother of repeatedly laying 
off 8. One diagram meeting this requirement is derived in Fig. 221, 
where the figure made up of the reference line GH, the eccentric radius 
OE, and the t line ES is rotated backward about through the angle 8. 
Then GH takes up the constant position MN, while OE coincides with 
the crank, and the perpendicular DF gives the value of t. If measured 





Fig. 222.— The Zeuner Diagram. 

upward from MN, parallel to OP, t is toward the right, or plus; if 
downward, or in the direction OQ, it is toward the left, or minus. This 
is the Reuleaux or ordinate diagram of valve movement. 

The derivation and form of the Zeuner or polar diagram are given 
in Fig. 222. We first develop, at I, a new way of representing the 
motion of the slide in terms of that of the driving crank arm (here the 
eccentric arm OE), as follows: 

On the line OB, which is the right-hand dead-center position of the 
eccentric, draw the circle OFB with r or OE as its diameter. Then the 
intercept OF, cut from OE by this circle, is equal to t; for the right- 
angled triangles OBF, EOS, are always equal, hence also the sides OF 
and ES. Inspection of the figure, or a few trial constructions, will show 
that when the eccentric lies across this circle, so that the intercept OF 
is cut from it directly, the valve is to the right: but when the eccentric 
has to be produced back through in order to cross the circle — that 
is, when it is anywhere in the semicircle HAG — the valve is to the 
left. Now, just as in Fig. 221, we change from a diagram in terms of 



364 VALVE GEARS AND GOVERNORS. [Chap. VIII. 

eccentric position to one in terms of crank position, by rotating 
backward about O, through the angle 5, the figure made up of the 
circle OFB and the eccentric radius OE. Then, in II, the circle takes 
a constant position on the diameter OD, and the eccentric is brought 
into continual coincidence with the crank. The intercept OF cut from 
the crank by the valve circle measures t, to right or left as it is direct 
or indirect. 

The geometry of both these diagrams is very simple: but practice 
and familiarity are needed to give facility in using and understanding 
them. A simple model, in which the crank-eccentric COE is made 
actually to rotate over either diagram, is a help at first in making it 
clear that the perpendicular DF in Fig. 221 or the intercept OF in Fig. 
222 II, is always equal to ES. But after this has been clearly realized, 
the eccentric should be discarded, and the diagrams thought of only as 
showing a direct relation between crank angle and valve position. Not 
only do these diagrams give the length and direction of t, but we can 
see which way the valve is moving by noting whether t increases or 
diminishes as the crank advances, and can get an idea of the velocity 
of the valve by noting whether t is changing rapidly or slowly. 

(c) Rules for Drawing the Diagrams. — It is obvious that if the 
eccentric be placed on its right-hand dead center OB — when t will 
have its greatest plus value — the crank will be perpendicular to the 
base line MN of the Reuleaux diagram, and will lie along the valve- 
circle diameter of the Zeuner diagram. Then a rule for constructing 
the Reuleaux diagram would be: Draw an eccentric circle, of radius r; 
place the eccentric on its plus dead center and draw a diameter at 
right angles with the corresponding position of the crank: this will give 
the base line and determine the direction of -\-t. For the Zeuner dia- 
gram, place the eccentric on its plus dead center, and on the correspond- 
ing crank line measure off r and draw a valve circle on this radius as a 
diameter. These rules become general if we make the following as- 
sumptions: Let the initial dead center, from which to estimate crank 
angle, be that for which the piston is farthest from the crank shaft; let 
t be considered plus when it is from mid-position toward the shaft; and 
let the eccentric angle 8 be always measured from crank toward eccen- 
tric, in the direction of rotation of the shaft:* then no matter which 
way the engine stands or runs, and whether or not the lines of piston 
stroke and valve stroke agree, the above rules, and. the directional mean- 
ings of t as there stated, hold true. 

* An exception to this statement of general conditions is found in the case of 
the locomotive engine as usually viewed — see Fig. 229. 



§ 37 (c)] SIMPLE SLIDE VALVE, WITH HARMONIC MOTION. 365 

PROBLEMS 

1. With values of 5 near the middle of each of the four quadrants from 
deg. to 360 deg., draw motion diagrams of both kinds, and show on each the 
crank positions where the valve is at mid-stroke and where t has its greatest 
plus and minus values. In some of these diagrams, take the engine conditions 
to be other than those of Fig. 162, as to position and as to direction of turning. 

2. For given values of r and 5, draw a Reuleaux and a Zeuner diagram: 
and on each find where the crank is when t = +%r and t = — \ r. 

(d) The Complete Valve Diagram. — Having established methods 
for completely representing and determining the movement of the 
valve, we shall next consider how this valve, moving back and forth 
over the ports, effects the steam distribution. In Fig. 223 I, a com- 
mon slide valve is shown in mid-position on its seat ; and the controlling 
dimensions, besides r and 8 as represented at II, are 

s = outside lap, or steam lap; 
* = inside lap, or exhaust lap. 

Complete valve diagrams for the left port, or for the head end of the 
cylinder, according to the two methods, are given at III and IV. 

When the crank is at OM — in IV this line is tangent to the valve 
circle, so as to have a zero intercept — the valve is in mid-position. 
As the crank advances, the valve moves toward the right, the t ordi- 
nate being positive and increasing in both figures: when C gets to Q, 
where t = Qq = cO = s, the valve edge and port edge are just in line, 
or the port is just beginning to open. For the crank on dead center, 
the valve takes the position shown at V; the travel is t and the port is 
open by the small amount e, which is called the lead. When the crank 
is at any position OC, to which VI corresponds, we have t = CF = EO : 
and it is evident that, in general, the port opening is equal to (t — s). 
In order to make a graphical subtraction of s from t, we draw in III the 
lap line QR parallel to MN at the distance s; and in IV, draw the lap 
circle cKd, with s as radius. Then the segment QDR and the crescent 
cDd are identical diagrams of port opening. We see that admission 
begins — or, we " have admission " — at Q, maximum opening is at D, 
and cut-off takes place at R. It is evident that the determining of 
admission and cut-off is simply a matter of finding crank positions for 
which the valve is at a certain distance from mid-position. 

After the crank passes R, the valve keeps on moving back from the 
right — as is shown by a plus but decreasing t — until it again gets to 
mid-position when the crank is at ON: then it goes toward the left, and 
soon opens the exhaust port, this occurring when t = —i. The be- 
ginning and end of exhaust, or " release " and " compression," as also 



366 VALVE GEARS AND GOVERNORS. [Chap. VIII. 

the port opening during exhaust, are found by drawing the exhaust lap 
line TS or the inside lap circle fOe. In IV, instead of using only the 
plus valve circle on OD, we save overlapping by drawing another valve 
circle on OD', for which the direct intercept shows left-hand or minus 
travel. This is convenient but not necessary, since it is evident that 
OT is determined equally well by either intersection, e or e'. In find- 
ing release and compression from the Zeuner diagram, the beginner is 
likely to confuse the intersections of valve circle and inside lap circle, 
especially when, as is usual, only the one valve circle is drawn. Keep 
clearly in mind, not only that the valve must be at a certain distance 
for one of these events, but also to which side it must be, and which 
way it must be moving. Thus, with the positive valve circle alone, if 
we were to draw a crank line from through f for the release position, 
we should make a mistake : for while the valve is at the distance i, it is 
toward the right; whereas it should be to the left and moving to the 
left, as is the case when the crank is at eOT. For these short-lap 
measurements the Reuleaux diagram is clearer and more accurate than 
the Zeuner. 

On the exhaust side of this valve there is over travel; for if we 
measure off the port width 6, and draw VW parallel to ST, and the 
circle hkg at the distance b from the lap circle, we see that the valve 
travels more than enough fully to open the port. Sometimes there is a 
slight over travel on the steam side : but more frequently — and most 
of the time in single-valve gears with variable cut-off — the maximum 
opening for admission is much less than the width of the port. 

For the other port, or the other end of the cylinder, the events and 
conditions are diametrically opposite to those shown, with a symmet- 
rical valve: if the laps are not equal, they must be drawn in, and the 
required intersections found. Generally, both sets of lap lines should 
be drawn on a Reuleaux diagram, dotting those for the crank end. But 
in the Zeuner diagram, we usually draw but the one valve circle; and, 
with equal laps, the same intersections serve for both ports. 

4 

PROBLEM 

3. For given values of r, 5, s, i, and b, draw a complete diagram by each 
method, showing on it the steam distribution — especially admission, cut-off, 
release, and compression — for both ends of the cylinder; and test for com- 
pleteness of opening and for over travel on both steam and exhaust sides. 

(e) Valve and Piston Diagrams. — Having established simple 
methods for finding the relation between the positions of the valve 
and of the crank, our next step is to extend these to the valve and 
piston. The primary, determining diagrams are shown in Fig. 224, 



§ 37 (e)] SIMPLE SLIDE VALVE, WITH HARMONIC MOTION. 



367 



where the valve diagram (of either form) is combined with the piston- 
position diagram from Fig. 163: then DC and CF are simultaneous de- 
terminations, to be used, respectively, as ordinate and abscissa in Fig. 
225 — compare the similar combination in Fig. 169. The distortion 
from symmetrical steam distribution caused by the action of the con- 
necting rod, notably the inequality in the cut-offs, is well brought out 




V H 



V H 



Fig. 223. — Valve Diagrams. 



by this figure; but can be rather more clearly seen on the derived dia- 
gram given as Fig. 225, where the valve travel is plotted on the stroke 
line as a base. 

The curve got by this method is elliptical in form, and with harmonic 
motion for the piston as well as the valve it is a true ellipse. The 
effect of the connecting rod is here shown by dotting in parts of the 
simpler curve. The lap lines are now drawn parallel to MN: and the 
four events, admission, cut-off, release, and compression, are located by 
the intersections marked A. B, C, and D, respectively. Dotted lines 
and primed letters are for the crank end of the cylinder. 



368 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



In order to equalize the cut-offs, making them the same as with 
harmonic piston movement, the laps would have to be changed to the 
values Si and s 2 , as marked on the figure. This would reduce the lead 




Fig. 224. — Combined Diagrams for Valve and Piston. 

— which is shown by the distance from Q to the point where the curve 
is tangent to the end line — almost to zero at the head end, while nearly 
doubling it at the crank end, besides changing the widths of the port 







Fig. 225. — The Valve and Piston Diagram. 

openings all through both admission periods. A diagram of this type 
furnishes the most satisfactory data for a comparison of valve action 
with realized steam distribution, as shown by the indicator; and this 
matter of symmetry of action will be more fully discussed farther on. 

For an autographic diagram, to be drawn by the engine and to serve 
as a test of the working of the valve gear, especially with releasing 






§ 37 (c)] SIMPLE SLIDE VALVE, WITH HARMONIC MOTION. 



369 



gears of the Corliss and similar types, this elliptical curve is the most 
convenient, the motions necessary in the apparatus being the same as 
in the steam-engine indicator. 

(/) Lap, Lead, and Angle of Advance. — The evolution of the 
engine valve is illustrated in Fig. 226. The simplest possible case is 

Z 4 ^ 




Fig. 226. — Evolution of the Valve. 



shown at I, where the valve just covers the port when in mid-position, 
and is driyen by an eccentric at right angles to the crank, so that its 
mid-position coincides with the dead center. This arrangement has 
the very decided fault that the admission is too long, the port being 
open during the entire half-revolution, or the whole stroke of the piston, 
as shown by the Reuleaux diagram at II. 

To shorten the period of opening, the first step is to give the valve 
a lap, so that it will not uncover the port until the eccentric has turned 
through a certain angle from the vertical, and will close it at the same 
angular distance before the other mid-position, as in III. Along with 
this change, the eccentric must be advanced beyond the position at 
right angles to the crank, so that when the latter is on dead center the 
valve will be at a distance from its mid-position equal to the lap plus 
the lead. The effect upon the diagram is shown at IV; in V the valve 
is sketched, and what is often called the angle of advance, y = (6 — 5o), 
or (8 — 90°) in the usual engine, is determined by the relation 

OD = s + e = rsin(5-90). ..... (204) 

An important deduction from this figure is, that if the admission is 



370 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



to be very short, the lap must be very large relative to the radius, 
and the width of port opening correspondingly small. This matter, 
together with the changes in the action of the valve on the exhaust 
side, will be considered when we come to valve gears with a variable 
eccentric. 

(g) Two Types of Valves. — There are two typical forms of the 
slide valve, the flat and the piston form, and these are made with a 
great variety in detail. Examples of both have been shown in the last 
chapter, and a more detailed description will be found in § 42. Another 
distinction now. to be drawn, and one having to do rather with the 
present side of the subject, is illustrated in Fig. 227. The first ar- 
rangement, having the live steam at the ends and the exhaust in the 
middle, as in the plain flat valve, is called the direct valve; the second, 



II. 





s-*- s 



WWa 



Fig. 227. — Direct and Indirect Valves. 



with the steam in the middle and exhaust past the ends, and with 
the laps interchanged accordingly, is called indirect. Another way of 
defining the two types is to say that they have respectively dutside and 
inside admission. And a general distinction, applying equally well to 
single, separate-function valves, is expressed by stating that the direct 
valve opens inward, moving toward the middle of the cylinder, the 
indirect valve opens outward — referring particularly to the steam 
edge at either end. In other words, the direct valve opens the port by 
moving in the direction of the piston stroke for which this opening is 
a preparation, while the indirect opens against the stroke and closes 
with it. 

The effect upon the position of the eccentric, due to a change from 
the direct to the indirect valve, is shown in Fig. 228: the necessary 
reversal of each valve-travel distance is secured by reversing the 
eccentric in II into a position diametrically opposite to that which 
it occupies in I. These are the characteristic eccentric settings for 
the two types of valves. In II it is simpler to estimate 5 as a nega- 
tive angle, rather than to measure it all the way round in the plus 
direction. 



§ 37 (h)] SIMPLE SLIDE VALVE, WITH HARMONIC MOTION. 371 

(h) Effect of a Reversing Rocker Arm. — Sometimes a rocker 
arm pivoted at or near the middle is interposed between the eccentric 
and the valve. The result of this is brought out in Fig. 229, which is 
drawn for the locomotive, where the cylinder and axle interchange the 




3 o 
Fig. 228. — The Two Eccentric Settings. 

characteristic positions for the stationary engine, as given in Fig. 162, 
but the zero dead center is still taken at the left. To compensate for 
the reversal of motion by the rocker arm, the eccentric must be diamet- 
rically reversed on the shaft; so that with a direct valve it has the 
setting proper to the indirect, and vice versa. In this case, however, 



6 




^v 



Jj\ if v' 

D 

Fig. 229. — The Reversing Rocker Arm. 



it is usual to disregard the reversal in the mechanism, and to draw the 
valve diagram as for an unreversed eccentric, in the usual position. 
It is evidently from its analogy to this effect upon the eccentric setting 
that the name " indirect valve " is derived. 



§ 38. Various Valve-gear Relations 

(a) The Bilgram Diagram, while less simple in idea than either of 
those developed in the last section, is quite a little used, and the student 
should understand it. In Fig. 230, MN and OD are the same lines as 
in Figs. 221 and 222. If N is taken as a center or pole and a perpen- 
dicular NK is dropped upon any crank line, COK, the distance NK is 
the valve travel t : it is a simple matter to trace out the equality of the 



372 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 




Fig. 230. — The Bilgram Diagram. 



three triangles NKO, OFD, and CEO, thus showing that the Bilgram 
vector NK is the same as the Reuleaux ordinate CE and the Zeuner 

vector OF. To see whether the 
valve is to right or left, stand at 
O and look along the crank line 
toward C: if N is off toward the 
right from OC, the valve is to the 
right of mid-position. Lap circles 
are drawn with N as center, then 
tangent crank-line diameters lo- 
cate admission at OQ, cut-off at 
OR, release at OT and compres- 
sion at OS. 

The dotted circle on ON is the 
locus of the point K; it is closely 
analogous to the Zeuner circle, and 
the vector is of the same character, but is measured from the outer 
end of the radius r or ON, instead of from the inner end. The fol- 
lowing trigonometrical relations are easily traced out, a being always 
the crank angle AOC : 

In Fig. 221, ZEOS = ZDOF = (a + 8)- 90, 

then ES = DF = * = r sin EOS = r cos (a + 8). 

In Fig. 222, II, ZDOF = (180 - 5)-> - 180 -(a + 8), 
then OF = t = r cos DOF = r cos (a + 8). 

In Fig. 230, Z NOK = (8 - 90) + a = (a + 8)- 90, 
then NK = t = r sin NOK = r cos (a + 8). 

(b) Geometrical Relations. — 
Certain geometrical properties of the 
valve diagrams, which have frequent 
application in problems upon the 
working of the valve as represented 
by these diagrams, are illustrated in 
Fig. 231. 

1. If the crank be placed on its 
zero dead center OA, the particular 
position OE of the eccentric radius and 
the line OD will be symmetrical with 
respect to the vertical GH. And if the 
crank be turned to OB, then OE' and 
OD are symmetrical with respect to AB . Fig. 231 . — Geometrical Relations. 




§ 38 (&)] VARIOUS VALVE-GEAR RELATIONS. 373 

2. By drawing the two diagrams together, the identity of their 
determinations is made apparent : as also the fact that a crank position 
dependent upon a short valve travel, as OS or OT, is much more accu- 
rately located by the Reuleaux diagram than by the polar. Even 
when using the Zeuner diagram alone, we make an accurate determina- 
tion of S and T by drawing ST tangent to the lap circle and at right 
angles to OD. 

3. A perpendicular from D upon AB cuts off a length OF equal to 
the steam lap plus the lead. Conversely, if we measure off (s + e) 
and erect a perpendicular, this line is a locus of D. The comple- 
mentary relation for the eccentric is shown in Fig. 226 V, and stated in 
Eq. (204) : it is what determines the eccentric angle 5 in practical valve 
setting. 

4. The fact that DK is tangent to the lap circle is especially useful 
when we have a locus of D and wish to draw the valve diagram which 
will give a particular cut-off. 

5. The line DO bisects the angle of admission QOR and the angle 
of release TOS. 

6. A circle from A with the lead e as its radius is tangent to the 
line QR: self-evident on the Reuleaux diagram, this can be independ- 
ently shown for the Zeuner from* the equality of the right triangles 
AUO, DFO. 

Any event in the valve action can be located by giving either the 
crank angle at which it takes place, or the corresponding piston travel 
with infinite connecting rod. Thus the cut-off is fixed either by the 
angle AOR or by the ratio of AP to AB: but the admission line OQ 
can be located only by the angle of lead, AOQ or e. 

(c) Problems on the Simple Valve Gear. — The following 
resume of the symbols used in this discussion will be found con- 
venient : 

r = radius of eccentric, half of total travel of valve. 

I = length of eccentric rod. 

5 = eccentric angle, measured from crank toward eccentric in direc- 
tion of rotation. 

t = valve travel, or distance from mid-position at any instant. 

s = steam lap, outside on a direct valve, inside on an indirect. 

i = exhaust lap. 

b = width of steam port. 

e = lead, measured in port opening. 

e = angle of lead, plus when measured from admission line toward 
dead center. 



374 



VALVE GEARS AND GOVERNORS. 



(Chap. VIII. 



A few practical problems will now be given, all having a direct 
bearing on valve setting or design. Others can be devised, but many 
of them are useful only as illustrating the geometrical possibilities of 
the diagrams. 

PROBLEMS 

4. Given r, s, and e: find 6 and cut-off. 

5. Given r, e, cut-off, release: find 5, laps, and compression. 

6. Given r, e, cut-off, and compression: find 8 and release. 

7. Given s, e, and cut-off: find r and 5. 

(d) Valve Setting. — The amount of adjustment possible after 
the engine has been designed and built varies with the type of valve 
gear. In many single-valve engines, where the eccentric is carried by 
a shaft governor or where it is keyed to the shaft, everything depends 
on its being correctly designed: but sometimes the eccentric can be 
rotated on the shaft, so as to change the angle 5, and clamped in any 
desired position. In most engines the length of the valve rod or of the 
eccentric rod can be varied; and in the more complex valve gears there 
are likely to be a number of points at which this kind of adjustment 
can be made. 

The two conditions to be met are, first, that the valve movement 
shall be symmetrical, so that the steam distribution will be as nearly as 
possible the same for the two ends of the cylinder; second, that it shall 
be properly timed with reference to the motion of the piston. 

With the engine cold and the valve chest open, the two adjust- 
ments, of rod length and of eccentric angle, would be made together 
until the leads were equal and had the proper value — the engine being 

repeatedly placed first on one dead center, 
then on the other. Or, if desired, equal- 
ity of leads may be .partly sacrificed to 
equality of cut-offs. With the help of the 
indicator, the valve can be set with the 
engine in running condition, stopping it 
for adjustment after each trial. This lat- 
ter is, in many cases, the final method. 

(e) Change of Rod Length. — The 
effect of this adjustment is shown in Fig. 
232: the dotted lines show symmetrical 
working or equal laps, the full lines the 
result of lengthening the rod, in a direct- 
valve engine ; two circles being used so as to separate the indications for 
the two ends. Referring to Fig. 223 1, we see that to shift the mid-posi- 




Fig. 232. — Rod Length Changed. 



§ 38 (e)] VARIOUS VALVE-GEAR RELATIONS. 375 

tion to the left will increase s and i r } decrease i and s' — this notation 
distinguishing the ends just as does that used for the events on the 
diagram. Then for the head end, admission is shortened and ex- 
haust lengthened; while the opposite effects are produced in the other 
end. 

Adjustment under the indicator is illustrated in Fig. 233. As 
shown by I, there was quite an inequality in the cut-off and in the 
power developed in the two cylinder ends: this could also be detected 



I. 





Fig. 233. — Valve Setting with the Indicator. 

by the sound of the exhaust puffs. Through uncertainty as to the 
type of valve, the rod length was at first altered in the wrong direc- 
tion, with the effect shown at II. Reversing this, and correcting in 
the proper direction, the symmetrical steam distribution represented at 
III was secured. 

The matter of proper setting of the eccentric will be discussed in 
connection with the Corliss valve gear. In any case, a thorough under- 
standing of the working of the mechanism is fundamental to an in- 
telligent treatment of faults in its operation. 

(/) Secondary Disturbances. — Under this heading may be men- 
tioned looseness of the joints of the gear and the angular swing of the 
eccentric rod. The former will cause the valve to make a little pause 
at each end of the stroke, and then lag behind its geometrical position 
by an amount equal to one-half of the combined play in the joints: 
this being true if friction of the valve is the predominant force, as 
against inertia, which would throw the valve outward from mid- 
position, or pressure of steam upon the end of the valve rod, which 
tends to keep the lost motion all taken up in one direction. 

The influence of rod swing can be directly shown on the Reuleaux 
diagram, by substituting for the straight reference line MN in Fig. 221 
an arc with the rod length I as radius — this being analogous to the 
curved tangent arcs in Fig. 163. The lap lines will then be " parallel " 
arcs of the same radius. This effect can commonly be disregarded; but 
a full discussion of it will be found in Steam Engine, Vol. II, pages 
202 to 296. 



376 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 




§ 39. The Shifting Eccentric: Variable Steam Distribution 

(a) Moving the Eccentric Center. — Following the line of de- 
velopment suggested by Fig. 226 III and IV, and carried forward in 
Relation 3 under Fig. 231, we see that if the center of the eccentric be 
shifted along a line at right angles to the crank arm, changing both the 

length and the inclination of the 
eccentric radius, the cut-off will be 
varied without changing the lead. 
This fundamental principle of the 
whole class of single-valve, vari- 
able cut-off engines (as well as 
several derived forms) is illustrated 
in Fig. 234. 

The eccentric is supposed to be 
carried on a cross slide keyed to 
the shaft, so that the center can 
be moved along the path EiE ; 
and is either clamped in any par- 
ticular position, or held in place by 
the governor. For the longest ra- 
dius OEi, the valve circle is on 
ODi; and all the events, cut-off at ORi, release at OTi, and exhaust 
closure at OSi, are late. 

The intermediate diagram is located so as to give cut-off at three- 
eighths of the stroke, by drawing KD perpendicular to the radius OR: 
and along with the change in cut-off go smaller changes in release and 
compression, all these events being made earlier by the increase of 8. 

The limit of movement of the eccentric is usually at E , on the 
crank line: and the corresponding steam distribution is shown by the 
circle on OD . The very small opening of the port, together with the 
great compression from So, produces a steam diagram whose effective 
area is not far from zero. 

(b) The Eccentric Pendulum. — Referring to Fig. 15, where a 
simple shaft governor is outlined and described, we see that what 
needs to be known from it, in order to determine valve movement, is 
the shape of the locus or path of the center E on the plane of the gover- 
nor — this locus being commonly an arc of a circle, traced by the end 
of a swinging bar or " pendulum," of which the position and displace- 
ment are determined by the equilibrium of the forces within the gover- 
nor proper. For valve-gear purposes, the required dimensions are 



Fig. 234. — Shifting Eccentric with 
Constant Lead. 



§39(6)] SHIFTING ECCENTRIC: VARIABLE DISTRIBUTION. 377 

shown on Fig. 235, where the different possible arrangements are given 
and a conventional method is developed for stating, as concisely as 
possible, the essential data. 




Fig. 235. — The Eccentric Pendulum. 



With the crank line CO and the perpendicular GH as axes, the 
pivot P is located by the coordinates a and b, the algebraic signs having 
the meanings indicated. In general, for any position of the crank, a is 
plus from O toward C, b is plus in the direction of the motion arrow 
through C. Then the pendulum radius Q or PE, and the limiting 
eccentric radius r\ or OEi, complete the data. In the absence of 
specific statement, E is supposed to be on the line CO. 

Of the four characteristic positions of P, numbers 1 and 2 belong to 
the direct valve, 3 and 4 to the indirect. The offset b may have any 
value from zero up to T\\ making it equal to half the vertical projection 
of ri gives the nearest approximation to the straight-line locus of Fig. 
234. In any case, drawing a line DF at a distance equal to the steam 
lap s from GH will show clearly how the lead will vary as E changes its 
position. 

(c) Diagrams from an Automatic Cut-off Engine. — In the 
example worked out in Fig. 236, the data are: a = -f-5|", b = +1J", 
Q = 6f", n = 2f", s = 1", i = 0. The eccentric locus, from Ei to 
the crank line, is divided into three equal parts, and four Reuleaux 
diagrams are drawn, a part of the lap circle helping to locate the several 
lap lines. The change in admission and cut-off is shown by drawing 
in the corresponding crank positions, while release and compression 
would be located by simply extending the base lines of the diagrams. 

The curves in Fig. 237 are plotted from the diagrams in Fig. 236. 
The four distances QE, Q'E', NH, MET, are all equal to the port 
width b, which is 2": and even with the full stroke of the valve the 
port is not fully opened for admission, though there is over-travel on 
the exhaust side in this one case. Curve No. 3 gives only a moderately 
early cut-off, and yet we see how small is the port opening, and how 



378 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



great an effect can be produced by even a slight change in the length 
of the valve rod. Note that in case 4, where the eccentric is in line 
with the crank, the motion diagram reduces to a single line, which 
would be straight with the piston in harmonic motion, but is here 
slightly curved. 

(d) Problems on the Shaft Governor. — The following data are 
from actual engines, as were those for Fig. 236. In each problem, get 
the eccentric locus first, and then draw valve diagrams for the greatest 




Fig. 236. — Valve Diagrams from a Shaft Governor. 

eccentric radius, for cut-off at one-third of the stroke, and for the 
earliest cut-off. One-third is chosen because it will give an effective 
cut-off, referred to the boiler pressure, at about one-quarter of the 
stroke ; and it is upon this cut-off that the rated power of the engine is 
based. The Zeuner diagram is rather better for illustration, the Reu- 
leaux for accurate determination of the whole movement. 



PROBLEMS 

8. Direct valve, a = +14", b = 0, Q = 15", r, = If", s = if", i = 0. 

9. Indirect valve, a=-l\", 6=-f",Q = 2f", n = If", s = 1&", i= |". 
10. Direct valve, a = +5|", & = +!", Q=6£", n = lf"s= 1", i=\". 

(e) Width of Port Opening. — Ideal valve action would be 
characterized by a very quick (practically " instantaneous ") move- 
ment in opening and closing the port, together with a very full width of 



§39 («)] SHIFTING ECCENTRIC: VARIABLE DISTRIBUTION. 



379 



opening. Figure 237 shows how far these requirements fail of fulfilment, 
especially when the cut-off is early. Let us suppose that in this par- 
ticular engine the width of the port is proportioned so as to give a cer- 
tain maximum velocity of steam flow, say 200 ft. per sec. — see § 42 (e) 
for the method of determining this width. The idea is that when the 
piston has its highest velocity, practically equal to the constant v of 
the crank pin, the current of steam flowing through the full port at 
200 ft. per sec. will just fill the volume being displaced by the piston. 
In other parts of the stroke, the flow along the port or passage will be 
slower: but in the curves Vi and V2 is represented the variable width 




Fig. 237. — Stroke-line Diagrams from Fig. 236. 



of opening, by the valve, that corresponds to a maintained speed of 
200 ft. per sec. for the steam. To get an ordinate at any piston posi- 
tion, multiply the port width by the ratio of actual piston velocity v 
(as in Fig. 166) to crank-pin velocity v : these widths are measured 
from the lap lines or port edges QR and Q'R' as bases. From a com- 
parison between the dotted and the full-line, actual curves, it is very 
evident that the actual velocity of flow past the valve must greatly 
exceed the assumed value of 200 ft. per sec, especially at early cut-off, 
with consequent large drop in pressure toward cut-off. Another point 
is, that the opening ought to be a little greater at head end than at 
crank end, on account of the somewhat higher velocity of the piston 
in the first part of the forward stroke. 

(/) Symmetrical Admission. — In Fig. 237, the mean or equal cut- 
offs for curves 1, 2, and 3 are marked by short vertical lines: as in Fig. 
225, it appears that in order to locate the act of valve closure at the 
same relative position in both strokes, it will be necessary to use a 



380 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



larger steam lap at the head-end port than at the crank end. But 
equality in effective cut-off, as denned in § 19 (d), or in the amount of 
steam admitted to the respective ends of the cylinder, is far more im- 
portant than to have the valve close at the same fraction of both 
strokes. Considering the higher piston velocity in the forward stroke, 
a very small unbalancing of the laps, in the direction just indicated, 
will be enough to secure equality in m.e.p.: its amount can be de- 
termined only with the help of the indicator, the adjustment being a 
simple matter of change of rod length, as in § 38 (e). 

(g) Indicator Diagrams. — To illustrate variable steam distribu- 
tion by the slide valve, the steam diagrams in Fig. 238 have been made 




Fig. 238. — The Variable Steam Diagram. 

up. They correspond with the timing of events in Fig. 237, but are 
laid out in close imitation of actual indicator cards. The extra diagram 
A is drawn for valve closure at one-fourth of the stroke, which, how- 
ever, makes the effective cut-off a good deal earlier. The curves are, 
of course, smoother than those traced by the indicator, especially with 
high-speed engines. 

The most important things shown in Fig. 238 are the locus QQ of 
valve closure as related to pressure, the locus TT of the point of re- 
lease, and the manner in which compression changes with cut-off — all 
of them characteristic of the type of engine under consideration. 
Curve QQ has a large share in determining the relation of power (or of 
m.e.p.) to valve action and, back of that, to governor position. Its 
general form is rational, but any attempt at a close preliminary layout 
can be made only by applying experience with other engines of similar 
design. 

The realized performance of any shifting-eccentric valve gear can 
be clearly shown by a combination of diagrams like that in Fig. 238, 



§39(0)] SHIFTING ECCENTRIC: VARIABLE DISTRIBUTION. 381 



with perhaps some derived curves representing the variation of m.e.p. 
with cut-off, or of cut-off, compression, and m.e.p. with the position of 
the eccentric center on its locus. 

The influence of speed of running, in modifying the steam distribution 
effected by a given valve action, has been well illustrated in Fig. 99. 

(h) Influence and Variation of Lead. — The matter of pro- 
portioning this element of the valve action so as to get the best re- 
sults is one that can hardly be reduced to definite terms. In general, 
two objects are to be kept in view: first, to have the engine run smoothly, 
without a too abrupt reversal of pressure at the end of the stroke; 
second, not to waste any of the possible area of the steam diagram by 
late admission. As regards the first, nothing need be added to the 
brief statement at the end of § 34 (c), except to say that a " negative " 
lead may be called for under certain conditions. As to the matter of 







^r — 


<^~~ — Q 




V? 


V. II. 









<^ IV. 







Fig. 239. — Different Ways of Varying the Lead. 

getting full steam pressure before the piston begins its stroke, it is 
evident that rotary speed, clearance volume, and height of compression 
all exert influence. In any case, the angle of lead — a measure of time 
— is rather more important than the exact width of opening at the in- 
stant of passing dead center. In an engine where the admission is 
controlled by a fixed eccentric, this angle will usually lie between 5 
and 10 deg. 

Engines of the shifting-eccentric type, with the shaft governor, show 
considerable variety in the location of the pivot point P, Fig. 235, and 
in the manner of variation of the lead. As typical cases in this respect, 
consider the diagrams sketched in Fig. 239. The point P is on the 



382 VALVE GEARS AND GOVERNORS. [Chap. VIII. 

same side of the center in both I and III ; but in the first case it lies on 
the crank line, in the second it is on a parallel line through Di. The 
valve diagram in I is drawn for cut-off at one-sixth of the stroke; and 
through the large lead quite a wide opening of the port is secured, even 
with this very early cut-off. In III and IV, the mechanical cut-off, or 
instant of complete closure, is at one-quarter stroke: the greater drop in 
pressure, due to throttling on account of the small opening, is clearly 
shown, especially by the lower position of the curve QQ. 

One advantage of the arrangement at III is that the governor can 
completely shut off steam from the engine, which it cannot do with 
the proportions in I. Further, the eccentric moves through a some- 
what smaller distance, for a given range of power, in III than in I. It 
is suggested by the steam diagrams, II and IV, that the question as to 
the best method of governing the engine under small loads is here in- 
volved — this question being, whether it is better to throttle the steam 
or to make the cut-off very early. In view of what has been shown in 
§§22 and 23 as to the harmful effect of excessive expansion and com- 
pression, it is likely that a light-load diagram of the type at IV may 
give better economy than that at II. 

§ 40. Reversing Valve Gears 

(a) The Stephenson Link Motion. — The derivation of this most 
common type of reversing valve gear is at once suggested by consider- 
ation of the eccentric settings for opposite directions of rotation, shown 
in Fig. 240. If the two eccentrics are put on the engine shaft side by 



Fig. 240. — Eccentric Settings for both Directions. 

side, and if the control of the valve can be transferred from one to the 
other at will, the engine can be made to run in either direction. What 
was logically the primary type of a device for making this transfer is 
that shown in Fig. 241, where by moving the lever R either hook, Bi or 
B 2 , can be made to engage the pin at V. This crude arrangement 
preceded the link motion, and was used on hoisting engines: it has, of 
course, been entirely superseded. 



§ 40 (a)] 



REVERSING VALVE GEARS. 



383 



The substitution of the curved link for the " gabs " of Fig. 241 is a 
radical improvement, not only on account of its mechanical superiority, 
but because it adds a second very important function to that of merely 




Fig. 241. — The Gab Motion. 

reversing the engine, in making possible a regulation and variation of 
the steam distribution very similar to that effected by the movable 
eccentric of the shaft governor. 

(6) Form of the Link Motion. — This valve gear is used on 
locomotives, marine engines, hoisting engines, and rolling-mill engines. 
The example in Fig. 242 has quite an extensive transmission gear be- 
tween the link and the valve, the rod 6, bent to clear an axle, running 
forward to a rocker such as is outlined in Fig. 229 and in Fig. 244. In 
the other lines of service named, the valve rod is generally driven 
directly by the block, giving the simpler scheme in Fig. 243. 

The valve gear as a whole divides itself into several component 
parts. The link motion proper, from the shaft or main axle to the 
link 4, including the suspension rod 13, forms one complete mechanism, 
with definite motion; the adjusting gear, pieces 14 to 16, constitutes 
another division; the valve connections, comprising everything from 
the block 5 to the valve, make up a third. The link in Fig. 242 is of 
the offset type; that is, the pin connections for the eccentric rods are 
set well back of the center arc of the link. The hanger pin projects 
backward from a saddle which is bolted to the link and is so formed as 
not to interfere with the passage of the block. The block pin is fast 
on rod 6 (on the rocker in Fig. 244), and has a bearing in the block. 
In marine engines the rod pins are commonly on the center line of the 
link, by which arrangement some minor disturbances of movement are 
eliminated: the block slides between two curved bars, which are at its 
sides instead of its front and back as in Fig. 242, while the eccentric 
rods are forked so as to engage joint pins on the outside of these bars; 
and thus the block can get clear out into line with either rod. 



384 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



The reverse-lever system, or the adjusting gear, controls the power 
of the engine, by raising and lowering the link so as to change the 
position of the block in the link, and thereby vary the steam distribution. 
By means of a latch on the, reverse lever, engaging notches on the 




Fig. 242. — A Locomotive Valve Gear. 



1. 
2. 
3. 
4. 
5. 
6. 
12. 



Eccentric. 
Eccentric Strap. 
Eccentric Rod. 
Link. 
Block. 

Extension Rod. 
Hanger Pin. 



20. Bearing for Hanger. 



13. 


Suspension Rod. 


14. 


Lifting Shaft. 


15. 


Reach Rod. 


16. 


Reverse Lever. 


17. 


Notched Arc. 


18. 


Balance Spring. 


19. 


Extension-rod Hanger. 



arc 17, the valve gear can be locked at any setting. In the casing 
numbered 18 is a compression spring, which balances the weight of the 
link motion, so that the reverse lever will move easily in either direc- 
tion. The radius of the link arc is equal to the length of the eccentric 



§ 40 (&)] 



REVERSING VALVE GEARS. 



385 



rods; if then the axes of the two eccentric straps could be brought to 
the axis of the shaft and held there, the link could be moved baek and 
forth without changing the position of the valve — except as the 
tipping of an offset link will change the effective distance (parallel to 
the valve stroke) between an arc through the rod pins and the center 
arc of the slot. This particular degree of curvature therefore reduces 
practically to zero any effect which the shape of the link might have 
upon valve position, and leaves the mechanism free to reproduce and 
combine, at the block, the motion of the eccentric centers. 

(c) Arrangement of the Rods. — The two typical general forms 
of the link motion, differentiated by the manner in which the block 
drives the valve, are outlined in Figs 243 and 244 — both turned about 




Fig. 243. — The Direct Link Motion. 



into the characteristic locomotive position. The effect of the reversing 
rocker arm, as set forth in Fig. 229, and further indicated by the dotted- 
line eccentric settings in Fig. 240, is here shown in the reversed position 
of the crank, with reference to the figure of the eccentrics, in Fig. 244. 
These diagrams are also intended to 
make clear the distinction between 
the two possible arrangements of 
the eccentric rods, or two ways of 
connecting the eccentrics to the 
link — that between " open " and 
" crossed " rods. During a whole rev- 
olution of the shaft, the two rods 
will be part of the time clear of each 
other, as here, part of the time 
crossed, as in Fig. 242. The dis- 
tinction is made by turning the shaft 
so that the two eccentric centers Ei 
and E 2 are toward the link, or 
between the link and a vertical center line through 0; and then noting, 
for this characteristic position, whether the rods are open, as shown by 
the full lines, or crossed, according to the dotted lines. 

(d) Movement of the Valve. — The following method of repre- 




The Indirect Link Motion. 



386 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



senting the action of the link motion is not quite exact, because some 
small secondary movements of the link are not taken into account. 
Further, the proof of the statements as to proportionality along the 
eccentric locus and as to the shape of that locus is too long to be given 
here. A full discussion of the kinematics of the link motion, including 
the modified Gooch and Allen gears, will be found in Steam Engine, 
Vol. II, pages 220 to 241. The approximate method for the Stephenson 
gear, quite good enough for all ordinary purposes, will now be set forth. 
For any position of the block in the link, intermediate between Li 
and L 2 , the motion of the valve is very nearly what would be given by 
a single eccentric with its center on a curve through Ei and E 2 : the 
location of this center E between Ei and E 2 being similar — in the 
geometrical sense of proportionality — to that of B between Li and 

L 2 . To make this statement fit Fig. 
244 exactly, we should designate as 
Bi and B 2 the block positions right in 
line with the two eccentric rods, and 
make the proportionality apply to 
the location of B on BiB 2 . 

In Fig. 245 the first thing shown, 
at I, is the manner in which reversing 
could be secured by the movement 
of an actual single eccentric center. 
Having an eccentric pendulum piv- 
oted at P, extend its range of move- 
ment past E to E 2 ; then the lower half of the locus of E will corre- 
spond with, and will produce, reversed running of the engine. 

The locus of the equivalent single eccentric, for the link motion is 
shown at II and III of Fig. 245 for the respective cases of open and 
crossed rods. In strict accuracy parabolas, these curves are well 
enough approximated by circular arcs through the points Ei, E , and 
E 2 : the point E being located, or the length of the mid-gear radius OE 
given, by the formula 





III. 




>E 2 &E 2 

Fig. 245. — The Eccentric Locus. 



r 



= r( 



cos/3 ± ysinjSj; 



(205) 



where r is the actual eccentric radius, /3 is the supplement of 5 as on 
Fig. 245 II, k is half the length LiL 2 of the link, and I is the length of 
the eccentric rod. The plus sign is for open rods, giving the convex 
locus in II, or increased lead toward mid-gear; the minus sign and the 
concave curve are for crossed rods. Note that the second term of the 
formula, (k/l)r sin /3, is the amount by which the curve departs from 



§ 40 (<*)] 



REVERSING VALVE GEARS. 



387 



the straight line EiE 2 ; being the fraction k/l of the half-length of this 
Hne. 

The " adjustment " of the valve gear, or the position of the link upon 
the block,. is defined as follows: 

When the block is under the full control of either eccentric — 
that is, at Li or L 2 in Fig. 243, in line with Li or L 2 in Fig. 244 — the 
mechanism is said to be at " full gear," forward or backward. Mid- 
position is called mid-gear, as indicated above. Any other position is 
described by giving the fraction got by dividing the half-length of the 
link into the' distance of the block from the middle of the link: thus we 
speak of half gear, three-quarters gear, and so on. 

Positions of the reverse-lever latch on its arc will be almost exactly 
similar to those of the block in the link: so that the setting of the valve 
gear can be equally well denned in terms of that position. 

(e) Valve and Indicator Diagrams. — A sample set of valve 
diagrams for a Stephenson gear is given in Fig. 246. The eccentric 





Fig. 246. — Valve Diagrams for the 
Link Motion. 



Fig. 247. — Diagrams from a 
Locomotive. 



locus is first laid out at EiE E 2 (for the crank at zero), and the locus 
of D is made symmetrical to it, with reference to the line GH. Valve 
circles are drawn, for full gear forward, on ODi; for full gear backward, 
on OD 2 ; for mid gear, on OD ; and for half gear forward, on OD; OD 
and OE corresponding with a position of block in link halfway between 
Li and the middle, according to the definition just given. 

Several indicator diagrams from a locomotive are reproduced in 
Fig. 247. The largest, No. 1, shows the greatest amount of work per 
revolution that the engine is capable of performing; this would be done 
only at very low speeds, and the tractive force, or tangential force at 
the driving wheels, due to this steam diagram, would be so great that it 
would slip the wheels if friction were not increased by the use of sand 



388 VALVE GEARS AND GOVERNORS. [Chap. VIII. 

on the rails. The normal resistance of the train is represented by the 
smaller diagrams, taken at speeds of 35 to 75 miles per hour. Slight 
variations in boiler pressure and in the opening of the throttle valve, 
together with the influence of speed, account for the differences in the 
admission pressure, and render impossible the close determination of a 
cut-off locus like QQ on Fig. 238. 

PROBLEM 

11. Given r, s, k, and I, and that the rods are open. First set the eccentrics 
so as to have zero lead in full gear; then get the eccentric locus, and draw 
Zeuner diagrams for full gear both ways, for mid-gear, and for quarter cut-off 
forward. Show the steam distribution in each case, taking the inside lap to be 
zero. Good average data are, r = 2§", s = 1", k = 8", I = 50". 

(/) Idea of the Radial Gears. — The general principle of all 
gears in which a slide valve with harmonic motion from an eccentric is 
made to produce variable steam distribution is, to shift the center of 
the eccentric along a locus or path in the plane of the crank,* which 
locus approximates a straight line and lies at right angles to the crank 
line. In the shaft governor, the actual, physical eccentric is thus 
shifted. In the link motion, the variable eccentric is a geometrical 

resultant, got by proportional division be- 
tween two actual eccentrics which form the 
ends of the locus. In a third scheme, now 
to be described, the effective eccentric is 
the resultant of two radial driving arms 
at right angles to each other, one of them 
variable in length. 

The diagram in Fig. 248 shows the 

fundamental principle of what are called 

* 2 radial valve gears. To secure the desider- 

Fig 248 — Component and atum of a driving center E which can shift 
Resultant Eccentrics. . 

from Ei to E 2 , use is made of a fixed arm OE 

and a variable arm OE', the point E' changing position on a line parallel 
to EiE 2 . A mechanism is devised which will first produce a recipro- 
cating motion from the eccentric OE , and then add to this the motion 
from OE'; the combined effect will be that of the resultant arm OE. 
The center E is almost never an actual driving point, at the shaft, but 
the movement that would be given by OE is derived from the main 
crank OC (generally from the crosshead) through a system of levers : 

* That is, a plane perpendicular to the axis of the shaft, on which crank, eccen- 
tric, etc., are projected, and which turns with the shaft. 




§ 40 (/)] 



REVERSING VALVE GEARS. 



389 



for the OE' component there mayor may not be an actual eccentric at the 
shaft. A couple of examples will illustrate the working out of the idea. 
(g) The Walschaert Gear. — In Europe this is the most com- 
monly used valve gear for locomotives, and it has been coming into 
increasing use in this country. The outline in Fig. 249 will serve as a 




Fig. 249. — Outline of Walschaert Gear. 

sufficient illustration. Motion taken from the crosshead at J is re- 
duced and reversed by the lever KHL, taking H as the fulcrum: this 
gives the effect of a short arm opposite to the crank, like OE in Fig. 
248. The pin E, carried on a return crank from the main crank pin 




Fig. 250. — The Joy Valve Gear, as for a locomotive; at A, enlarged section of curved 

guide 5. 

and having OE as its radius arm, drives the oscillating " link " 3: the 
resulting movement, communicated through block 4 and rod 5 to the 
pin H, is made variable by shifting the block in and out from the fixed 



390 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



pivot P, and reversible by carrying B past P. The reverse lever acts 
on the lifting shaft 10, just as in the Stephenson gear, Fig. 242. 

(h) Geometrical Relations. — At I in Fig. 251, B D is the mid- 
dle position of the link, with crank on dead center, while Bp is the same 
as in Fig. 249. Let eccentric radius OE = r, DP = k , BP = k, also 
let maximum BP upward = ki and maximum BP downward = /c 2 . 
The displacement B B would come directly from an eccentric opposite 
to OE' in III, and of the length r f = r X (k/k Q ). At II, K L is the 
middle position of the lever 6, KLi shows it as if swung on a fixed pin 

c 

a 





Fig. 251. — Derivation of Equivalent Eccentric, Walschaert Gear. 

at H , and KL is the final position when H has been given the dis- 
placement H H = B B. For the lever 6, let 

LH LK 



HK 



= m, 



HK 



= (l + m); 



then the displacement L Li is equivalent to that from an eccentric 
OE (at III) of the length r = mR. The distance LiL is larger than 
H H in the ratio (1 + m), so that the component arm E E has the 
value (1 + m) r (k/ko). At the outer limits of block position, 



E E 1 =(l + m)r|i, 

/Co 



E E 2 = (l+m)r^- 2 . . (206) 



In the diagram III, amplified from Fig. 248, SF is L Li, FE is LiL; 
the proportions are not relatively the same as in I and II, because the 
crank is now in a different position from that in Fig. 249. 

PROBLEM 

12. In an engine of 24" stroke, the valve is to have a maximum travel of 
5", and lap plus lead or OE is to be 1": with r = 4" and k = 14" in Fig. 249, 
find the ratio m for the lever LHK and the lengths ki and k 2 of the halves of 
the link. 

(i) The Joy Valve Gear. — In this mechanism there is no actual 
eccentric at all, but both of the component effects in Fig. 248 are de- 



§ 40 (i)] 



REVERSING VALVE GEARS. 



391 



rived from the main crank, through the connecting rod. The floating 
lever DE or 2 in Fig. 250 has one end pivoted on the connecting rod, 
the other guided by the radius rod 1. Lever 3, driver by the pin G, 
oscillates with a motion nearly proportional to that of the main cross- 
head, and moves bodily up and down because of the swing of the con- 
necting rod. The first motion realizes the effect of the component 
eccentric OE , the second, through the slant of the guide or link JJ 
(which can be changed and reversed) , is turned into the direction of the 
valve movement, and becomes equivalent in result to a variable driv- 
ing radius E E. 

§ 41. The Double-valve Gear 

(a) General Considerations. — It has been made clear by 
Figs. 226, 234, and 236 that when early cut-off is secured with a single 
slide valve, the lap must be relatively very large and the port opening 
small; and that the compression must begin early in the return stroke, 
on account of the great angular advance of the eccentric. To prevent 
early compression from running too high, the clearance must be large; 
but while large clearance is incidental to the design, and unavoidable, 
in most high-speed engines, and while a good compression is mechan- 
ically advantageous when the inertia force of the reciprocating parts is 
large, a closer search for economy renders desirable a valve action 
which will not cut away so much of the possible effective area of the 
steam diagram as is lost, for instance, in Fig. 74. Simpler than the 
arrangements with separate valves and ports for admission and ex- 
haust, and with no limitations as to speed, the Meyer or double slide- 
valve gear is the first type which we shall consider as meeting the re- 
quirements of full port opening, quick cut-off, and the most favorable 
regulation of the exhaust operations. 



V c 








Fig. 252. — Meyer Valve with Variable Lap. 

(b) The Meyer Valve Gear. — In Fig. 252 the main valve V m 
is extended beyond the lap edges, so as to enclose the ports P, P; and 
on its flattened back rides the cut-off or expansion valve V e , which 
controls the passage of steam through the ports in the main valve. 



392 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



The latter determines the operations of admission, release, and com- 
pression, just like a single valve: it is driven by a fixed eccentric, and 
does not cut off until late in the stroke, so that it can give a good, full 
port opening. Early and variable cut-off is effected by the riding 
valve. Very frequently the latter is driven by a shaft governor; but in 
Fig. 252 is shown an adjustable device (not automatic), often used on 
air compressors, where the governor acts by throttling, and both eccen- 
trics are fixed. By means of right and left threads on the valve rod, 
the two parts of the expansion valve can be separated or brought to- 
gether so as to make the cut-off earlier or later. When adjusting, the 
clamping nut N is slacked off a little and the rod turned by the spanner 
wheel W until the indicator R is at the desired cut-off, as graduated on 
the slide S : then the nuts are screwed up tight. 

(c) Relative Movement of the Cut-off Valve. — In the dia- 
gram of the eccentrics, Fig. 253, E m is the center that drives the main 
valve, while E e drives the expansion valve; and the absolute movement 
of the latter, or its movement with reference to the fixed valve seat, is 
determined by the rotation of the eccentric radius OE e . We are inter- 
ested, however, not in the absolute position of V e at any instant, but in 
its position on V m : and this relative travel is got by thinking of V e as 
driven on V m by the eccentric radius E m E e , or r v . The geometrical 
relation involved is simply that SE e , the horizontal projection of E m E e , 
gives always the distance of the center line of V e from that of V m . The 

fact that this crank arm rotates about 
a moving point E m is immaterial; but 
this movement of the center of rotation 
can be eliminated by shifting r v to OE v , 
or to the opposite side of a parallel- 
ogram of eccentrics: then since S'E V 
is always the same as SE e , we have 
that V e would be driven on a fixed 
valve seat by OE v just as it is actu- 
ally driven on its moving seat by E m E e . 
The radius r v we call the virtual eccen- 
tric; and its angle 8 is measured off as indicated on Fig. 253. It will 
be noted that the two valves are never simultaneously in mid-position, 
as they are drawn for illustrative purposes in Fig. 252. 

(d) Functions of the Cut-off Valve. — It is required of this 
valve that, being out of the way when main-valve admission begins, so 
as to leave a clear passage into the port P, it shall then close this port 
quickly at some desired instant, earlier or later, in the stroke of the 
piston. Any crank-driven slide moves most rapidly when near the 




Fig. 253. — Relations of the 
Eccentrics. 



§ 41 (d)] 



THE DOUBLE-VALVE GEAR. 



393 



middle of its stroke; consequently, the cut-off valve must have a small 
lap if it is to be in rapid motion when closing its port. Very often the 
lap is negative, or the valve does not cover the ports when in mid- 
position, as is the case in Fig. 252. 

(e) Positive and Negative Valves. — Certain ideas fundamental 
to the whole matter of valve action are given concrete and complete 
expression in Fig. 254. By means of primary diagrams of the ordinate 




Effect of Varying the Lap. 



type (the simple eccentric diagram of Figs. 220 and 221), we emphasize 
the fact that the important result sought in any determination of valve 
motion is the movement of the valve edge with reference to the port 
edge, rather than of the center of valve with reference to center of 
seat — this by markedly substituting " the lap line QR for the center 
line GH as a reference line. Further, we show in II how with positive 
lap the period of opening is less than half a revolution, so that the 
single valve is necessarily of this type, on the steam side at least; while 
the valve with negative lap, or the negative valve, opens its port for 
more than half a revolution, and can therefore control only one opera- 
tion. Rotating II into the regular Reuleaux diagram position, we 
easily see that the eccentric driving a single valve must, of necessity, 
be in the second quadrant ahead of the crank if the valve is direct, in 
the fourth if it is indirect. 

(/) Eccentric Setting for the Negative Valve. — In Fig. 255, 
Zeuner diagrams are used to illustrate these same ideas, and to show 
how the eccentric setting for a negative valve is determined. I and II, 
for the positive valve, are entirely obvious; but we now lay especial 
stress on the facts that the crescent EDG is a diagram of port opening, 
and that the Cut-off intersection G determines the crank angle for which 
the valve is at the distance s to the right, but is moving toward the 
left. 



394 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



With the negative lap — s shown at IV let us require that the 
valve close the port when the crank is at OC in III. The lap circle is 
drawn with absolute radius s, algebraic sign having no immediate 
significance. For cut-off, the valve must be to the left, wherefore the 




Fig. 255. — Locating the Valve Diagram. 



-I -2 



valve circle must necessarily go through E instead of E': and the fact 
that the negative travel intercept must increase as the crank advances 
puts the circle in the full-line position on OD, as against that on OD'. 
The crescent EDL is now a diagram of port closure ; and we see further 

that it is characteristic of a negative cut-off 
valve, if of the direct type, to have its valve 
circle in the fourth quadrant, and its virtual 
eccentric in the third quadrant ahead of the 
crank. 

(g) Vaeying the Cut-off. — The action 
of the device in Fig. 252 is shown by Fig. 256, 
where cut-offs are determined for laps varying 
by quarters from minus three-fourths to plus 
three-fourths of the radius of the virtual eccen- 
tric. Through comparison with Fig. 255 III, 
the diagram is self-explanatory. One point to be noted, especially 
marked for the cut-offs designated +3 and —3, is that the valve edge 
approaches the cut-off position more rapidly from the negative than 
from the positive side, the curvature of the valve circle showing this 
very clearly. Another point is, that with a large negative lap the 
period of closure is short ; so that if the cut-off is very early, the expan- 
sion valve may reopen its port before the main valve cuts off. This 




Fig. 256. — Control by 
Variable Lap. 






§ 41 (g)] 



THE DOUBLE-VALVE GEAR. 



395 



possibility exists only with extreme proportions, and belongs rather to 
the method of regulation typified in Fig. 257. 

In Fig. 257 I, with a negative lap equal to half of r v , the valve 
circle is located for cut-off at 0.1, at 0.3, and at 0.5 of the stroke: and 
at II is given a diagram showing how the center E 2 of the expansion 
eccentric will have to be rotated about Ei in order to secure this effect. 
It is a simple matter thus to pivot the second eccentric at the center of 
the first, and place it under the control of a shaft governor of suitable 
design. A wider range of cut-off would be covered than is here shown : 




Fig. 257. — Rotating the Virtual Eccentric. 

and it is apparent that the eccentric must be rotated by the governor 
through an angle equal to the crank angle between earliest and latest 
cut-off. 

The scheme of Fig. 257 is the simplest case of varying the virtual 
eccentric, with the advantage that the second valve has a constant 
length of total travel upon the first valve. Another center can be 
chosen if desired, but the rotation of the cut-off eccentric about it will 
then cause a change in the length of the virtual eccentric. 



PROBLEM 



i" 

8 J 



n = J"; for the 



I'm 



With these data make the 



13. For the main valve, let r m = 2", 8 m = 120 
cut-off valve, virtual eccentric r v = 1\" } 8 V = 210°. 
following constructions : 

A. Draw the diagram for the main valve, and show the entire steam dis- 
tribution as determined by that valve. 

B. Draw the virtual diagram for the expansion valve, and find the cut-off 
when s v = — \" . 

C. Drawing the two diagrams together, determine and show by sketches 
the positions of the two valves when the crank is at deg., 45 deg., 90 deg., 180 
deg., and 270 deg.: indicate by arrows the direction of movement of each valve, 
showing both the absolute and the relative motion of the riding valve. 



396 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



E. Make s v = +§", 0", -1", and -11", and for each lap find the cut-off, 
as in Fig. 256. 

F. Keep r v = II" and s y = — 1", and change the eccentric angle so as to 
get cut-off at |, &, and | of the stroke. 

Draw separate figures for each requirement; use Zeuner diagrams. 

(h) Indicator Diagrams from engines with the double-valve 
gear are given in Fig. 258. The first set was taken from an engine 
with a load that fluctuated continually and widely, the effort to follow 
it keeping the governor dancing. The several expansion curves traced 
are selected from a large number of closely-spaced lines: constant 
compression and a quite sharp cut-off are the distinguishing features of 
these diagrams. At II the admission pressure drops as the piston 
speeds up toward mid-stroke, probably because the ports in this rather 
old engine are inadequate in size; but the cut-off curve is still quite 




Fig. 258. — Indicator Diagrams from Engines with the Double-valve Gear. Engine 
I, 16 by 24 in. at 145 r.p.m.; II, 16 by 32 in. at 110 r.p.m., both in power serv- 
ice; III, air compressor, 10 by 12 in. at 145 r.p.m. 

short. Rather different diagrams, with late admission and very short 
compression, are shown at III. Compare with all these the Corliss 
engine diagrams in Figs. 274 and 275. 



§ 42. Details of Slide Valves and Gears 

(a) Characteristics of Valves. — The simplest possible plain 
slide valve is that used for illustrative purposes in Figs. 14 and 223: it 
makes provision only for the essential functions of the steam distri- 
bution. In practical application, this primary valve is modified and 
complicated along two lines: usually the valve is " balanced," or ar- 
ranged so that it will not be forced hard against the seat by steam 
pressure; and very often the valve is so formed that it will admit steam 
past several edges, or is made " multiple-ported." The examples given 



§ 42 (a)] 



DETAILS OF SLIDE VALVES AND GEARS. 



397 



here, together with those shown in some of the cylinder drawings at the 
beginning of § 36, are to be considered from the two points of view 
just indicated, namely, 

First, as to form, with reference to the functions of steam distri- 
bution, and including the steam passages to the cylinder. 

Second, as to balance and tightness, and incidentally the possibility 
of relieving excessive pressure in the cylinder. 

(b) Various Forms of Valve. — Figs. 200 to 202 and 259 to 263 
illustrate the following descriptive classification : 

1. The short, single-faced valve, with long cylinder ports, Figs. 200 
201, and 262. This valve, mostly used in locomotives, has a balance 
rig on the back or top of it, working under a flat balance plate which is 
fastened to the steam-chest cover so as to be held parallel to the valve 
seat. 




Fig. 259. — The Balanced Flat Valve, with parallel faces and double admission. 
A, Horizontal section; B, Cross section; C, Face of valve. 

Valve seat. 3. Distance strips, a very little thicker 

Balance plate, very stiff against steam than the valve. 

pressure. 4. Spring, to hold plate in place when 

Valve. steam is off. 



2. The long, double-faced valve, with short ports, Fig. 259. This 
works between valve seat and balance plate, with a very positive and 



398 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



very accurate mechanical fit. In long cylinders, and especially when 
the steam and exhaust ports are made separate, it is usual to divide the 
valve into two short slides, each under its own balance plate. 

3. The double-seated valve, Fig. 202. In this arrangement there 
are really two complete valves and seats, the valves being set back to 

back and fitted together with a 
cylindrical, telescopic joint: the 
valve is indirect, having steam on 
the inside. The very long ports 
are a disadvantage of this scheme. 
4. The B valve, Fig. 260, is 
sometimes used in small steam 
pumps : the essential characteristic 
is that with the steam-chest ar- 
rangement of the direct valve, it 
has the movement of the indirect; 
this may be desirable in a gear of the type of Fig. 288. 

5. The solid-plug piston valve, as in Fig. 9 and Fig. 263. In small 
engines (say up to 6 in. diameter of valve), the valve is often thus made 




Fig. 260. — The B Valve. 




Fig. 261. — Piston Valve for Locomotive, with built-up style of construction: 
cylinder 20 by 28 in. Scale 1 to 8 and 1 to 4. 

1, 3. Heads, held together by rod. 4. Bull ring or face ring* 

2. Valve body. 5. Packing rings. 

solid and finished to a close running fit : under favorable conditions (no 
grit and regular lubrication) the valve may run for a long time without 
enough wear to cause serious leakage. Sometimes adjusting devices 
are added, so that the valve can be expanded or the seat bushing con- 
tracted, to take up wear. 

6. The packed or self-adjusting piston valve. In Fig. 261, there is 
at each end a solid bull ring (as on an engine piston like Fig. 206) and 



§ 42 (&)] 



DETAILS OF SLIDE VALVES AND GEARS. 



399 



two overhanging spring rings — note how these are restrained by a 
narrow ledge, so that in case of breakage the pieces cannot get out 
into the ports. Besides rings which thus form the valve edges, com- 
mon square rings, in grooves set a little way back from the edges, are 
often used. 

(c) Multiple-admission Arrangements. — In Fig. 202 there is, 
as already remarked, simply a combination of two valves into one. 
The valve in Fig. 259 readily gives double admission, since it naturally 
uncovers two edges, and only a small port through the valve is needed 
to make the outer edge effective. Figure 262 shows how an equivalent 




Fig. 262. — German Locomotive Valve with Allen Port. Scale 1 to 15. 



result is got with a one-faced valve, but now a long extra passage, 
formed in the body of the valve, is required. Let the direct valve of 
Fig. 262 move to the right, or the indirect valve of Fig. 263 to the left: 
at the same time that the regular edge uncovers the port, the edge of 
the inner passage (at the other end of the valve) runs off the valve seat, 
so as to admit steam into this passage. 

In general, the use of multiple-admission arrangements is much less 
common with the piston valve than with the flat valve. One of the 
purposes of the piston valve is to get long admission edges, with mod- 
erate overall dimensions and without complexity of arrangement. 

(d) Balancing Devices. — The flat valve in Fig. 259 and the solid 
piston valve in Fig. 263 are examples of what may be called rigid bal- 
ance, dependent for tightness upon original accuracy of form and fit, 
and upon the prevention of wear. They are incapable of rising from 
the seat to relieve excess pressure in the cylinder : for while the valve in 
Fig. 259 is not mechanically constrained, the area of balance plate sub- 
jected to steam pressure is so great that a very high pressure in the 
port would be needed to push the valve away from its seat. 

A flexible balance, as in Figs. 200 and 262, is less delicate, in con- 
struction and in service, than the arrangements just noticed, and is 
therefore far more suitable for the exacting conditions of transportation 
service, whether locomotive or marine. In Fig. 201, the fence or wall 
around the relieved area is made up of four strips which fit tightly against 



400 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



each other at the corners; note that the enclosed space is vented to 
the exhaust port. In Fig. 262 the relieved area is circular, as also in 
Fig. 202. Since the tightness of these valves depends upon their being 
pressed down on the seat by steam pressure, the area of relief is gener- 
ally made something like 60 per cent of the whole area of the valve face, 
leaving the other 40 per cent more or less subject to the pressure of the 




Fig. 263. — Piston Valve of the Allen Type. 



steam. When a port is partly open, for admission, nearly or quite the 
full pressure acts upon the under face of the overlapping part of the 
valve, thus diminishing the effective unbalanced area. 

(e) Design of Steam Passages. — The determining factor for the 
cross area of the port is the permissible velocity of the steam current. 
As the piston advances, the product of area A by instantaneous velocity 
v is the rate of volume generation by the piston; and in the steam pas- 
sage, area a by steam velocity V is the rate of flow to fill the new vol- 
ume. In terms of known quantities, then, the velocity V is 



T/ A 

V = ■— v. 
a 



(207) 



It is customary to proportion the ports for a maximum steam veloc- 
ity of 160 to 240 ft. per sec, this maximum occurring near mid-stroke, 
where the piston is moving a trifle faster than the crank pin. Using 
1.6 as the ratio of maximum to mean velocity of the piston — compare 
the statement preceding Eq. (150), page 293 — the range from 600 to 
900 ft. per minute of mean piston speed corresponds with from 16 to 
24 ft. per second of maximum velocity. In practice, the ratio of port 
area a to piston area A varies from one-tenth to one-eighth, in engines 
to run at from 500 to 800 ft. per minute of piston speed. 



§ 42 (e)] DETAILS OF SLIDE VALVES AND GEARS 401 

In engines where the prevailing cut-off is early, the maximum speed 
of flow is seldom or never reached by the entering steam ; but it always 
occurs during exhaust, hence this operation has the stronger determin- 
ing influence; and if the ports are separated, as in Figs. 3 and 265, the 
exhaust port is made larger than the steam port. With a high ter- 
minal pressure, at the end of expansion, a great part of the exhaust 
steam will escape in the first release, while the piston is moving very 
slowly, and thereafter the velocity of the steam is definitely related to 
that of the piston. 

Referring to § 16 (e), we see that the pressure drop required to pro- 
duce the above-named velocities, through an ideal orifice, would be 
very small — far less than the loss between the steam chest and cylinder 
usually observed in engines. But other resistances have a greater effect 
than does the inertia of the steam : and this range of steam velocity has 
.been found by experience to embody a good compromise between ex- 
cessive pressure drop on one hand and excessive clearance volume on 
the other. 

(/) Proportioning the Valve. — The width of port having been 
fixed', the laps must be determined: this involves the whole question of 
steam distribution, and would be worked out by the methods of the 
preceding sections. With dimensions decided upon for the single face 
that covers one port, the combination into a complete valve is a simple 
matter, unless there is likely to be interference of function. Referring 
to Fig. 200, it is evident that if the valve is moved very far to the 
right, the inner or exhaust edge of the left face will begin to throttle 
the opening into the main exhaust port; so that there is a limit to the 
shortening of the valve. The B valve, Fig. 260, is subject to a similar 
and stronger limitation. In some of the more complex slide valves, not 
here illustrated, where there are several openings into one port, this 
question of preventing interference becomes a chief determinant of 
proportions. 

(g) Eccentric and Strap. — One example of these parts has been 
outlined in Fig. 242, while fuller detail is given in Fig. 264. The 
larger side of the eccentric disc or sheave is very much in the form of a 
wheel, with one or more arms. For large engines, the sheave is almost 
always in two parts, joined by bolts with nuts or keys. Cast iron is the 
usual material in stationary engines, with the smaller " half " some- 
times of wrought metal; for locomotive and marine engines, cast steel 
is much used. In Fig. 242 the eccentric is secured by a key and set 
screws, while in Fig. 264 set screws alone are considered sufficient, and 
give an opportunity to change the setting of the eccentric. 

The bearing between eccentric and strap, if not carefully fitted and 



402 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



kept well lubricated, may be one of the most troublesome bearings in 
an engine. The bearing surface is nearly always cylindrical (an ex- 
ception being shown at H in Fig. 264), with recesses at the edges to 
make room for collars on the strap. In cruder lines of construction, 
there is a bearing of cast iron on cast iron, as indicated at E in Fig. 264; 
but it is better to line the strap with babbitt metal or brass, and with 
steel in sheave or strap this becomes necessary. Brass liners are shown 
at H and J in Fig. 264. 




Fig. 264. — Eccentric and Strap for Corliss Engine in Fig. 3, to fit shaft in Fig. 215. 
Scale 1 to 14. Sketches E to J, various sections of the eccentric strap. 

In that figure, the round eccentric rod passes through a yoke which 
projects from the strap, and is fastened by two nuts, one in the recess 
within the yoke. Very often a T end is formed on the rod and it is 
bolted to the strap, in an arrangement closely analogous to the marine 
type of connecting-rod end shown in Fig. 2. The locomotive, as in 
Fig. 242, has stiff rods, of deep rectangular cross section, very strongly 
fastened into a nose on the strap : there is much possibility of failure of 
lubrication, and the rod must be strong enough to keep the strap turn- 
ing on the sheave, even against a high resistance. 

(h) Rods, Rockers, Etc. — In some valve gears, notably on loco- 
motives, the rods are made with solid forged ends, the eyes or bearings 
being lined with hardened steel bushings and the pins case-hardened. 



§ 42 (h)] DETAILS OF SLIDE VALVES AND GEARS. 403 

On most stationary engines, adjustable rod ends are used, similar to 
those of connecting rods, with brass bearings. As shown in Fig. 269, 
at the rod 5, the end or head is most frequently a separate piece, into 
which the rod body screws; by using right and left threads, with lock 
nuts, and providing a hold for a wrench, adjustment of length is made 
easy. 

Occasionally a small slide block is used at the inner end of the eccen- 
tric rod, corresponding with the crosshead; but the rocker arm, of 
which examples have been quite fully shown in Figs. 5 and 6, is much 
more common. As to the function of the rocker, it may simply guide 
a joint as in Fig. 12, may change amplitude of motion as in Figs. 3 and 
267, or may reverse motion as in Figs. 229 and 244: further, it may be 
used to transfer motion sidewise from one plane (perpendicular to the 
shaft axis) to another. With such transfer, the direct rocker takes the 
form of the letter U, the indirect of Z. 

§ 43. The Corliss Valve Gear 

(a) The Corliss Cylinder. — A representative example, with 
valves of the simplest form, is shown in Figs. 265 and 266; in the end 
view some of the valve-gear parts appear. Note how the T head of the 
valve stem or spindle is engaged in a slot in the end of the valve, and 
how the yoke extending from the valve bonnet forms a support and 
bearing for this spindle. The wrist plate is carried on a heavy stud 
which is bolted to a seating on the cylinder. 

(6) The Valve Gear of this engine is shown in Fig. 267, partly in 
skeleton: the mechanism on the cylinder is made most prominent, but 
the shaft outline (the crank-eccentric COE) and the rocker arm are 
drawn in true proportions at A and B. By means of eccentric rod 1, 
rocker arm 2, and reach rod or hook rod 3, motion almost harmonic is 
given to the point H on the wrist plate 4; and we may say that this 
piece oscillates in practically harmonic motion, conceiving its angular 
movement as determined by the linear movement of H. The reach rod 
is not permanently connected to the wrist plate, but merely hooks over 
the pin, so that the valves can be moved by hand, with " starting bar " 
S, in starting and stopping the engine. 

Through the valve rods 5 and 7 and the cranks 6 and 8 the valves 
are given an oscillation which is far from harmonic. Intentionally, the 
opposite angular displacements of any valve arm, from a mid-position 
determined by putting the eccentric at 90 deg., are made very unequal. 
This is clearly shown in Fig. 270, where the mechanism is drawn in this 
mid-position and the range of movement of each C-point is marked. 



k 



404 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 




Fig. 265. — Lengthwise Section of Corliss Cylinder, 26 by 48 in. Scale 1 to 21. 




Fig. 266. — Cross Section of the Cylinder in Fig. 265. Upper right-hand quarter 
taken at mid-length, the rest of the section through -the head-end ports. 

The result sought and obtained is, that the valve shall have a wider 
and quicker movement in the direction for opening, a shorter and 
slower movement on the closure side. 



§ 43 (c)] 



THE CORLISS VALVE GEAR. 



405 




Fig. 267. — Corliss Valve Gear, Single-eccentric Type, with Full Wrist Plate. 



1. Eccentric rod. 

2. Rocker arm. 

3. Reach rod. 

4. Wrist plate. 

5. Steam-valve rods. 



6. Oscillating cranks. 12. 

7. Exhaust-valve rods. 13. 

8. Exhaust-valve arms. 14. 

9. Steam-valve arms. 15. 

10. Hook claw. 16. 

11. Cam ring. 



Governor rods. 
Governor rocker. 
Dashpot rod. 
Dashpot plunger. 
Dashpot body. 



(c) The Cut-off Mechanism. — The releasing gear for the head- 
end steam valve is shown in detail by Fig. 269. Valve arm 9 is merely 
dotted in, although the hook pin P, carried by it, is drawn in full. At 
B the several cranks are shown as if swung into one vertical plane, 
which involves a distortion of 6 ; and to save overlapping the hook claw 
or latch 10 is represented only by its center line. All the valve rods 
have heads like that on 5, and are adjustable in length by means of 
right and left threads, as are also the governor rods 12 and the drop 
rods 14. The relative positions and the different motion planes of the 
parts of the whole mechanism have already been illustrated in Fig. 266. 

The oscillating crank 6 has its bearing on the valve bracket or 
bonnet B. While it is turning toward the left, the valve is closed from 
the previous cut-off, and at rest; as 6 nears the limit of travel, the 
latch L slides over the catch pin P, going just a little way past the en- 
gaging point. As the crank is pulled toward the right it turns the 
valve stem with it, until the trip arm T strikes the knock-off cam Ci 
and L is pushed out so as to disengage P ; whereupon the dashpot pulls 
the valve quickly back to its rest position, giving a sharp cut-off. 



406 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



/' 




1. Governor standard. 

2. Governor spindle. 

3. Weight arms. 



Fig. 268. — The Governor. 

4. Lifting links. 

5. Lifting ring. 

6. Lifting sleeve. 

7. Lifting rod. 



8. Governor rocker. 

9. Dashpot rod. 
10. Dashpot. 



§ 43 (c)] 



THE CORLISS VALVE GEAR. 



407 



It will be noted that all the hooking and tripping surfaces are carried 
by small pieces of hardened steel, shaded on the figure, which can 
easily be readjusted or replaced — being held fast by small bolts or 
screws not fully shown on the drawing. A section of one dashpot is 
given in Fig. 267; it is of the double type, the inner plunger Pi being 
mostly concerned with the vacuum action, the annular plunger P 2 
with cushioning. A fuller description and discussion of the dashpot 
will be found in Art. (j). 

(d) Control of the Cut-off. — The manner in which the time of 
cut-off is determined by the governor, through movement of the cam 
ring 11, is apparent from Figs. 267 and 269. An important point is 
that the trip arm must strike the cam Ci before the crank 6 gets to its 




Fig. 269. — Detail of the Releasing Gear. 

limit of travel on the open side ; otherwise the valve will not be released 
at all, and steam will be admitted through nearly the whole stroke. 
This means that the latest cut-off operation under control of the gover- 
nor must begin a little while before the e'ccentric gets to its dead point 
— rapidity of closure then depending upon the strength of the dash- 
pot. As will presently be shown, this places the limit of controlled 
cut-off at from 40 to 45 per cent of the stroke in engines which have 
all their valves operated by one eccentric. 

The Governor. — This is of the vertical fly-ball type for a Corliss 
engine, the one from the machine under consideration being shown in 
Fig. 268, where view A is taken from the cylinder, looking toward the 
snaft, while B is a view from the front of the engine, or the side opposite 
the valve gear. The working of the governor mechanism is self-evident, 
the sleeve 6 being moved up and down as the centrifugal force of the 
balls varies with reference to the downward pull of their own weight 
and of the balance weight W; and the running speed can be changed 



408 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



by moving W in and out along its arm. The dashpot 10, with a loose- 
fitting piston working in oil, is of the drag or damping type, and is put 
on to keep the governor from responding too freely to small and irregu- 
lar impulses. The governor rocker 8 is the piece numbered 13 on 
Fig. 267. 

Action of the Safety Cams. — In Fig. 268 the whole mechanism is 
drawn in the starting position (for the engine standing idle), with the 
arm L resting upon the stop ring S. This gives the latest possible 
cut-off, without release, the trip arm T, Fig. 269, just working between 
cams Ci and C2. The ring S, freely turned by hand after the governor 




Fig. 270. — Diagram of the Valve Gear. 



has lifted, has a part of its upper edge cut away, as shown at C on Fig. 
268. When the engine is running, this notch is to be brought under 
L; then if through accident to its belt or for some other reason the 
governor ceases to turn, the balls will drop below the rest position, the 
safety cam C2 will be brought around so far as to prevent engagement 
of the valve arm and opening of the valve, and the engine will be shut 
down. Further, when the governor is at its highest position the knock- 
off cam Ci should release the valve before it is turned far enough to 
open the port, and thus prevent any admission of steam. 

This simple safety stop has the drawback that if through overload 
or fall of boiler pressure the speed drops below normal, the arm L will 



§ 43 (d)] THE CORLISS VALVE GEAR. 409 

sink into the notch in S, and the engine will be shut down. To prevent 
this, the engineer may not turn the ring into the safety position, thus 
depriving the engine of protection against the effect of an accident to 
the governor. More fully developed devices connect the support for L 
to an arm at the end of which is a small idle pulley riding on the gov- 
ernor belt; if the belt breaks, the stop is pulled aside, and the governor 
can drop to the low position and shut off steam. 

(e) Movement of the Valve. — In Fig. 270, the mechanism on the 
cylinder is drawn in mid-position, or with the eccentric at 90 deg., and 
a series of other positions is plotted, for the eccentric at equally-spaced 
angles. The results, in the form of ordinates which represent the 
linear travel of a point on the circular valve profile, relative to a fixed 
point on the seat, are laid out in Fig. 271, with the developed or un- 
rolled eccentric circle as base. For the steam valves we at first disre- 
gard the releasing gear, either imagining the oscillating crank to be fast 
to the valve stem, or considering that we determine the movement of a 
point on this crank projected out from the valve face. The dimensions 
necessary for a layout of the valve gear are shown on Fig. 270 : this par- 
ticular example was measured up from the actual engine, and it will be 
noted that the valve rods are adjusted to different lengths. 

The circle on AB is first drawn, with a radius equal to that of the 
eccentric when reduced to the upper end of the rocker arm, or when 
multiplied by the ratio GD/FD from Fig. 267. Swing of the eccentric 
rod may be disregarded, and the horizontal movement of the pin H be 
taken as harmonic. Then an angle scale for the movement of the 
wrist plate is got by dividing the eccentric circle and projecting the 
points of division to the path of H. For clearness of drawing, this 
path is moved down to MN, on an arc struck from 0' with a radius 
equal to OH. 

The four driving points Di, D 2 , D3, D 4 , being all on the same circle 
with H, this travel scale MN is next centered on each one : where two 
paths overlap, as is the case with Di and D 2 , one scale is marked out- 
side, the other inside, of the circle. The positions of the C-points are 
now found by striking off the rod lengths, and are then projected 
radially upon the circles representing the profile of the full cross section 
of the valve. 

Figure 270 is the picture of a drawing in which the mechanism as 
a whole was laid off half size, but the valves drawn full size: then the 
actual travel of the valve surface is given by the operation last de- 
scribed, and it is only necessary to rectify the curved path in order to 
have the desired ordinates of travel. For this purpose a scale of inches 
laid off on the valve seat, here marked on the inside of each circle, and 



410 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



used in connection with the horizontal ruling on Fig. 271, is most con- 
venient. 

The movement curves got by plotting the several sets of ordinates 
are given in Fig. 271, I and II for the steam valves, III and IV for 
the exhaust valves. The angle scale at the top of the diagram is 
the same as that on the circle AB in Fig. 270. Travel in the direc- 
tion which opens the port is represented by an upward ordinate for 
the head-end curves I and III, by a downward ordinate for II and IV. 
The distortion from harmonic motion is very clearly shown by these 
curves. 



90 120 150 180 210 240 270 300 330 



30 60 



90 



Ins. 






































Vl 














HI/ 








































/ 








r 


v. 


























I 


I. 


















/ 




















V 




7" — 






















































v 


^ 


k 






































































\ 


\ 






































































J 


V 














TT 


T- 














































^ 


V 


\ 


\ 








11 


1. 








" 




/ 


































\ 


















/ 


/ 






















































*ii. 










Tst 

























Fig. 271. — Valve-movement Curves. 



(/) Eccentric Setting and Valve Action. — Having drawn the 
simple curves of valve displacement in terms of eccentric position, our 
next step is to combine with these the lap of the valves — measured in 
the usual way, in the position shown on Fig. 270 — and thus find out 
the proper setting of the eccentric with reference to the crank. For 
present purposes it is enough to consider one end only of the cylinder, 
wherefore curves I and III are reproduced in Fig. 272. It is the opera- 
tion of exhaust that determines the eccentric setting, because both ends 
of this period have to be considered, as against only the beginning of 
the period of admission. Usually the lead for release, the angle TOB 
on Fig. 223, is less than the angle of compression, so that a small posi- 
tive lap on the exhaust valve is necessary: this is represented by the 
distance of the line TS above the base line, being here one-quarter of an 
inch. Since the lead for admission must be less than that for release, 
the steam lap must be larger, and QR is drawn at three-eighths above 
the base line. We now locate suitably the dead-center positions of the 
crank, A for head end, B for crank end, and find the angle 8 to be about 



§ 43 (/)] 



THE CORLISS VALVE GEAR. 



411 



106 deg. or the angle of advance about 16 deg. — this by noting that 
when the crank is at A or zero, the eccentric is at 106 deg. on its scale 
as marked below the base line. 

The Cut-off Action. — Instead of following the movement repre- 
sented by the whole of curve I, the steam valve really moves according 
to the full-line curves 1, 2, 3, or 4, of which the portion CDE shows 




Fig. 272. — Diagrams for the Head-end Valves. 

quick closure under the pull of the dashpot, and the straight line EF 
the period of rest while waiting for the next admission. These curves 
are merely sketched in from general considerations, since a mathematical 
determination of the action of the dashpot, while not incapable of 
giving quite accurate results, would be, in length and complication, 
rather out of proportion to the importance of the subject. Only a 
roughly approximate calculation would be made in working out a 
design, to adapt the results of experience to the particular case. 

Valve and Indicator Diagrams. — The steam-valve curves from Fig. 
272 are redrawn in Fig. 273, upon the stroke line of the piston as base, the 



O 30 



60 



360 330 

Fig. 273. 



90 



120 



150 180 



\ 




,2 


X3 


\d 


\4 






"*' 


-^ 


\ 


s "v. 






1 1 


\ 
























> 




^ 


^N. 








F^-> 


^E 



































K 
300 270 240 210 180 

Stroke-line Diagrams for the Steam Valve. 



piston positions being found as in Fig. 163 or Fig. 224. With these are 
to be compared the autographic diagrams in Fig. 274 I, which were 
taken from this same engine, being drawn by a pencil moved by the 
drop rod and working on the drum of an indicator which was con- 



412 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



nected to the ordinary reducing motion from the crosshead. Simul- 
taneous indicator diagrams are given at II. For the head end, the two 
types of diagram agree very well in proportions, the short vertical lines 
showing where cut-off takes place. These are first located on II, then 
transferred to I with due regard to the difference in length of the dia- 
gram. The crank-end diagrams were evidently not really taken at the 
same time. 

The characteristic Corliss-engine diagram is well represented by 
Fig. 274 II : the distinguishing features are, a horizontal admission line, 




L 



III. 




Fig. 274. — Indicator Diagrams from the Engine in Fig. 267. 

a sharp and usually rather early cut-off, release deferred till near the 
end of the stroke, and a compression curve which begins late but rises 
rapidly on account of the small clearance. At III is shown what 
happens when the boiler pressure drops so low that the engine cannot 
keep up to speed under its load, and the releasing gear fails to act — 
the steam consumption per revolution being now much greater than 
when the plant is working properly. 





Fig. 275. — Faults in the Eccentric Setting. 

A great deal of the valve setting to be done on a Corliss engine 
consists simply in adjusting the lengths of the various rods. Fig. 
275, however, shows faults in the setting of the eccentric: at I it needs 



§ 43 (/)] 



THE CORLISS VALVE GEAR. 



413 



to be advanced, at II we see the effect of advancing it too far, apparent 
especially in the excessive lead shown by the outward slant of the 
rising admission lines. 

(g) Valve Resistance in the Corliss Gear. — The amount of 
work that must be expended in moving a set of Corliss valves is small, 
not so much because the valves are not at times pressed very hard 
upon their seats as because the movements under this heavy pressure 
are small. The steam valve does resist strongly while being opened; 
but it need not be closed by any greater amount of overlap than re- 
quired to insure tightness — Fig. 272 showing more closure travel than 
is really necessary. When it is once open, any single-function valve is 
balanced or left free to move easily by the substantial equalization of 
pressure all around it. For the exhaust valve especially there is a 
decided gain in a marked distortion from harmonic motion. Referring 
to Fig. 272 we see that the period of rest and of slow movement of this 
valve coincides with the time when the steam pressure in the cylinder 
is high ; and the wide and rapid movement takes place after the pressure 
has been lowered by expansion, and while the port is open. 




Fig. 276. — Various Steam Valves: I. Passage through Valve; II. Murray Valve; 
III. Brown Valve; IV. Reynolds Valve. 

(h) Various Forms of the Corliss Valve. — The sections in 
Figs. 276 and 277, with Fig. 265, illustrate the following points: 

1. If the steam valve opens by an inward motion across the port 
(like the direct slide valve), as in Fig. 276 I and III, the drop rods being 
on the inside of the valve stems, the engine has outside admission; the 
opposite arrangement, in Figs. 265 and 267, and at II and IV of Fig. 



414 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



276, gives inside admission. With outside opening, the steam has a 
little longer path to traverse; and the purpose of the passage through 
valves I and III of Fig. 276 is to make this path as short and direct as 
possible. 

2. In Fig. 276 II and Fig. 277 III (both from Fig. 3), double open- 
ing is secured with a single port, by using the principle of the B valve, 
Fig. 260, for the second opening. 




Fig. 277. — Various Exhaust Valves: I. Plain Single-ported Valve; II. Fleming 
Valve; III. Murray Valve; IV. Reynolds Valve; V. Brown Valve; VI. Valves in 
Head of Cylinder. 

3. Double-ported valves are given in Fig. 276 III and IV and in 
Fig. 277 IV, V, and VI. Besides benefiting the steam distribution, 
the purpose of all these designs is to decrease the movement of the valve 
gear, thus adapting the engine to easy operation at higher speeds. 
The usual limit for Corliss engines is from 110 to 120 r.p.m., although 
the gear can be operated definitely, if not quietly, at as much as 150 
r.p.m. 

4. The exhaust valve is contained within the engine cylinder, so 
far as steam space or clearance volume is concerned. Valves I and II 
in Fig. 277 are made hollow and bulky, so that they fill all of the space, 
within the cylinder of the valve, that is not needed for the passage of 
steam; while valve No. V is moved up into the cylinder space, where it 
just nicely clears the piston when fully closed. No. II shows an at- 
tempt to make the valve close the port which enters from the cylinder, 
instead of, or in addition to, that which opens into the exhaust chamber; 



§ 43 WI- 



THE CORLISS VALVE GEAR. 



415 



the probability of success in this effort, depending upon the maintenance 
of a tight fit, is low. 

5. In large engines, especially when vertical, the valves are com- 
monly placed in the heads, as in Fig. 277 VI; this makes the ports 
short, and greatly simplifies the cylinder casting. 

(i) The Use of Two Eccentrics. — As already stated in Art. (d), 
the valve must be released before the eccentric gets to its dead point; 
and in Art. (/) it is shown that an eccentric to drive exhaust valves 
must have some advance, usually 15 to 20 deg. This condition is 
represented in Fig. 278 I, where 8 has the minimum value 105 deg., 
and it is assumed that latest dependable release must take place 15 deg. 
before dead center of the eccentric, or when the crank is at 60 deg.: 
this corresponds very closely with curve 4 on Fig. 272. 




Fig. 278. — Diagrams of Eccentric Setting. 

A very obvious way to increase the range of cut-off is to set the 
eccentric back, toward the crank, so that it will turn through a larger 
angle from the position for crank on dead center to that for latest 
release. In Fig. 278 II the negative advance or the angle of lag is 
25 deg., and the latest cut-off begins with the crank about at 100 deg. 
It is entirely evident that this eccentric can be used for the steam 
valves only. 

The limit to the setting back of the eccentric is found in the fact 
that if the negative lap is made too great, the valve will not cover the 
port effectively when closed. Thus in Fig. 278 III, CiOEi is the crank 
eccentric from II in the position for beginning of admission, and we see 
through what a small distance the valve has moved from its rest position 
— a distance which is all the smaller if there has been much distortion 
from harmonic motion on the closure side. The last diagram brings 
out further the absolute necessity of insuring that a gear of this type 
shall never fail to release: for the condition which produced the indi- 
cator diagrams in Fig. 274 III would in this case keep the valve open 
until the crank got around to C2, or far into the exhaust period. 



416 



VALVE GEARS AND GOVERNORS 



[Chap. VIII. 



A fairly obvious scheme for getting a longer range of controlled 
cut-off with one eccentric is to give the trip cams a cyclical motion, 
instead of simply having them held in one position by the governor. 
Then even after the valve arm has begun to return from its extreme 
position, the moving cam may overtake it and release the valve. 
This idea is applied in at least one design of power engine, and in 
several pumping engines — see Steam Engine, Vol. II, pages 320 
to 324. 

(j) The Dashpot. — The primary function of this device is to 
exert a sharp and strong force, which will close the valve quickly; the 
name comes rather from the secondary function of cushioning the 




Fig. 279. — A Two-plunger Dashpot. 



movement, or bringing the parts quietly to rest. A dashpot essen- 
tially the same as that in Fig. 267 is shown in Fig. 279: sometimes a 
single plunger is used, but with the double arrangement there seems to 
be more ease and flexibility of control. 

As the plunger rises, a partial vacuum is formed beneath it, and 
some air is drawn in; as it nears the bottom of the cylinder, on the 
drop, this air is compressed and furnishes the needed counterforce. 
On the inner cylinder there is first the adjustable valve Vi, next the 
check valve V2; so that the egress is made freer than the ingress, be- 
cause the downward movement is quicker than the rise. The inner 
plunger is intended to exert the stronger vacuum action, the outer is 
more concerned with cushioning. Relative to the piston displacement 
which it serves, the valve V3 is larger than the other two together, so 
as to permit readier inflow of air and cause a stronger checking of the 
descent. Both as to form and proportions, this device is based very 
largely upon experience and trial. 



§ 44 (a)] VARIOUS VALVE GEARS. 417 

§ 44. Various Valve Gears 

(a) Releasing Gears with Gridiron Valves. — There are a 
number of standard engines having a steam distribution exactly equiv- 
alent to that of the Corliss gear, but using flat gridiron valves. In 
location of valves (on top, at side, or at bottom of cylinder), and in 
form and detail of mechanism, these show a wider variation than do 
the more numerous designs which have been developed from the 
original Corliss. Sometimes the valves are short and wide, serving 
only two or three openings into the port, oftener they are narrow and 
long (length being taken in the direction of movement), covering a 
large number of short openings which lie across the port. The piece 
which moves the valves may be a reciprocating slide driven by an 
eccentric in the usual fashion, a shaft parallel to the engine axis and 
receiving an oscillating motion from an eccentric whose rod drops ver- 
tically to an arm on this shaft, or a rotating lay shaft, as in Fig. 282, 
which carries individual eccentrics at the valves. 

(b) Non-harmonic Gears with Shifting Eccentric. — To re- 
move the limitation of speed to which the releasing gear is subject, 
while retaining the advantage of non-harmonic motion with separate, 
single-function valves, engines are built with the cylinder and valve 
arrangement of the Corliss and allied types, but with the steam valves 
driven by a shaft governor while a fixed eccentric drives the exhaust 
valves. A steam valve thus controlling both admission and cut-off 
must give narrow port opening with early cut-off, just as does the 
slide valve. The extreme of development along this line is seen in the 
Mcintosh & Seymour gear, which has a double-valve arrangement on 
the steam ports; the riding valve is driven from the shaft governor, 
and all the valves are of the second gridiron form defined above. The 
engines represented by Fig. 97 are all of this design For analysis of 
these gears, see Steam Engine, Vol. II, pages 332 to 347. 

(c) The Lift-valve Engine. — For general power service, engines 
with lift or poppet valves have the same predominant position on the 
Continent of Europe that the Corliss engine has in American practice. 
The commonest arrangement of the valves, shown in Fig. 203, is similar 
to that of the Corliss cylinder in Fig. 265. Sometimes the valves are 
placed at the sides of a horizontal cylinder, or in the heads : and one or 
the other of these locations is used in vertical engines, the valve axis 
being always kept vertical, A very full description of the form and 
working of this gear, in all its variations, will be found in Steuerungen 
fiir Dampfmaschinen, by Leist. Only a few prominent points will be 
noted here. 



418 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



(d) Types of Valve. — Poppet valves are usually double-seated, 
and are so arranged as to be nearly balanced, only an annulus equal to 
or slightly exceeding the combined width of the contact surfaces being 
subjected to downward pressure when the valve is closed. The solid 
double-disc valve at I in Fig. 280 is the simplest in its own form, but 



m 



l> 



i. 






m x 




Fig. 280. — Different Types of the Two-seated Valve. I. Valve with double inlet ; 
II. Valve with single inlet; III. Bell or Cornish valve. 






requires a more complicated valve chamber, because the steam coming 
to it must be given access to both top and bottom, by means of pas- 
sages formed in the casting; but for a given diameter it has a larger 
capacity than the valve which receives steam from the top only, as at 
II. The latter, taken from Fig. 203, has the determining dimensions 
marked upon it: the effective opening is the area of the circle with 
diameter a, less the cross-sectional area of the valve; and the annular 
passages of the widths b and c should be given equal areas, so as to 
permit equal flow to or from both openings. Type III is derived from 
II by a kinematic inversion, the valve in one case corresponding in 
essential form with the seat in the other: it has the advantage that 
fitting the valve seat into the cylinder is a much simpler matter than 
with the double-contact arrangement in Figs. 203, 283, and 284; but it 
appears to require rather more room, so that the volume of the cylinder 
clearance will be greater. 

These valves as well as the inserted valve seats are made of hard 
cast iron. The contact strips or seats are narrow, ranging with the size 
of the valve, from one-eighth to one-half inch in width ; they vary from 
a 45-degree cone as in I to a plane surface as in III. Almost always 



§ 44 (d)) 



VARIOUS VALVE GEARS. 



419 



the valves are arranged to lift in opening, although engines have been 

built in which some of the valves open downward and are held up by 

springs. 

Sometimes single-disc poppet valves are used in the low-pressure 

cylinders of pumping engines. Thus the triple engine whose diagram 

is given in Fig. 131 I has these valves for ex- 
haust on the low-pressure cylinder; and the 

quadruple of Fig. 140, with eight sets of valves 

in all, has single-disc valves for the last three. 

For some large engines, four-seated poppet 

valves have been used successfully. 

A comparatively recent variation from the 

usual lift-valve practice (introduced about the 

year 1900) is shown in Fig. 281. These piston 

valves do not have to be brought to rest exactly 

at a certain level, and therefore require a less 

precise adjustment of the valve gear, if the 

latter cuts off by release: they open at only 

one edge, but with the greater facility offered 

for absorbing 
their momentum 
quietly, they can 
be lifted higher 
and dropped 
more sharply 

than the double-opening poppet valves, 
(e) General Arrangement of the 
Valve Gear. — With the valves located 
as in Fig. 203, the gear at the cylinder 
takes the form outlined in Fig. 282. 
In I, the large circle represents the bore 
of the cylinder, and the lay shaft is 
shown in section, with the two eccentrics 
at one end of the cylinder; II shows how 
Fig. 282. — Outline of Gear at Cyl- the shaft is driven by miter gears, and 

\ nd &> ^neral Arrangement as the eccentric setting is laid out at III. 
in Fig. 203. TT , , . i •/• ,i 

Here the crank is shown as it on the 

valve-gear shaft and at dead center, and each 5 as marked is meas- 
ured from the stroke line (the mean direction of the eccentric rod) 
to the radius arm OE. The steam eccentric OEi is only far enough 
ahead of the crank to take up the over travel of the latch in Fig. 
283, and give the valve a small lead when the crank is on dead center: 





Fig. 281. — Van den Ker- 
chove Piston-lift Valves. 



420 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 




Fig. 283. — The Collman Releasing Gear, Fig. 284. — Steam Valve and Gear, 42 by 
High-pressure Cylinder of Compound 60 in. high-pressure cylinder of en- 

Engine. Scale 1 to 8. gines in Subway Power House, New 

York. Scale 1 to 18. 

the exhaust eccentric OE 2 has about the same angle of advance (from 
a perpendicular to OH) as for a Corliss engine — somewhere near 
twenty degrees. 

(/) Admission Valves with Releasing Gear. — A first-rate 
German design is shown in Fig. 283. With the help of the detail at A, 
the arrangement of the driving mechanism is clear; at B we see how 



§ 44 (/)] VARIOUS VALVE GEARS 421 

piece 4 is made free to oscillate with the swing of 3. The forces which 
act to close the valve are the weight of all the parts attached to the 
valve stem and the push of the lower spring, here placed in the steam 
space. A rapid diminution of this force as the valve nears its seat is 
secured by the use of the lighter counter spring at the top; and the 
movement is checked by an oil dashpot, which has its plunger formed 
as better shown at C. The large holes let the oil pass freely while the 
valve is up, but only a small opening is effective when the valve is close 
to the seat. To avoid having the same oil resistance at the beginning 
of the rise as at the end of the drop, a number of small check valves are 
placed in a circle in the disc of the plunger, being made somewhat as 
suggested by the sketch at D. Air dashpots are sometimes used, and 
it will be noted that the lower end of the valve stem and guide on which 
the valve hub slides will act as a small dashpot with steam. Of course, 
to bring the drop valve quietly and yet quickly to its seat is a more 
delicate task than the closing of the Corliss or other sliding cut-off 
valve. 

In Fig. 284 the valve is raised by a rocking cam, carried on a spindle 
which is oscillated and released by the usual Corliss gear, with the 
dashpot on the side of the cylinder. The cam is forged solid with the 
spindle, and is forked so as to bear under the collar on both sides of 
the valve stem. Here the space under the lower end of the valve stem 
is relieved to the atmosphere, so that the steam may not get beneath 
the stem and tend to lift the valve. 

The mechanisms used for operating lift valves show a great variety 
in form. With Fig. 283, the exhaust valve is worked by a cam and 
lever. Cams of all kinds are used, and many ingenious linkage mechan- 
isms have been devised. As already noted, these are very fully given 
in Leist's book on valve gears. 

(g) The Engine without Crank Shaft. — In steam pumps and 
similar small engines which are described by this heading, special 
means of moving the valve must be adopted. It is not an effective 
scheme to make the piston operate its own valve through some sort of 
lever device, because the valve must make its wide and rapid move- 
ment at the time when the piston is moving very slowly, near the end 
of stroke. -In the duplex steam pump, this difficulty is surmounted by 
letting each piston drive the valve which controls the other cylinder. 
The essential part of the machine is drawn in Fig. 285, the cross view 
at the right showing the valve levers or rockers. It will be noted that 
lever 1 is direct, while lever 2 reverses the movement of the piston rod : 
they are both proportioned so as to give the same ratio of reduction of 
motion from piston to valve. The simple analysis of movement in 



422 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



Fig. 286 shows the working of this engine, and makes clear the need of 
levers of opposite character. 

In this figure, A marks the right side, B the left side. For position 
I, with piston A just reversing at left end of stroke, valve B (driven by 
arm A) is likewise at the left, port B is wide open at the right end, and 
piston B is moving from right to left; but in order that piston A shall 




Fig. 285. — Valve Gear of Duplex Steam Pump. 

presently move to the right, valve A must move to the right ahead of 
it, wherefore valve A must have a movement opposite to that of piston 
B. Following through the other three critical positions, and noting 
the directions of movement as indicated by arrows, we see that piston 
A leads, reaching any position half a stroke (one-quarter of the cycle) 
ahead of B. 







I «£. 9 




9 £ 



Fig. 286. — Valve Movement in the Duplex Pump. 

Although moved by the pistons, the valves are not closely driven, 
but there is always some lost motion between the rock levers and the 
valves. In Fig. 285 this clearance or back-lash is permitted at the nuts 
on the valve rod, on each side of the valve; on larger pumps, the same 
effect, with easier access, is provided for at the outer end of the rod. 
With positive connection, the valves would move too soon, so that 
the pistons could not make full-length strokes. Valve setting in a 
pump like this consists in putting the pistons at mid-stroke and the 
valves in mid-position, and then making the rod clearances the same 



§ 44 (g)] 



VARIOUS VALVE GEARS. 



423 



on both sides; minor adjustments may be found necessary after the 
pump is started, the object being to secure equality in the two strokes. 
Figure 285 illustrates the fact that in engines of this class the valves 
are made with nearly or quite a zero lap. It shows also the use of two 
ports at each end, the outer one for live steam, the inner for exhaust. 
By thus having the exhaust port open into the cylinder at some dis- 
tance from the head, a cushioning effect is secured, independently of 
the valve action, which will prevent 
the piston from striking the cylinder 
head. In order that this effect may 
be regulated at will (because less 
cushioning is needed at low than at 
high speeds), pumps of the larger 
sizes have stroke-regulating or cushion 
valves, arranged somewhat as shown 

by the sketch in Fig. 287. This valve varies the size of an opening 
through the wall between the two ports, permitting more or less 
exhaust by way of the outer part. Opening this valve lengthens the 
stroke, and vice versa. 




Fig. 287. — The " Dash-relief " 
Valve. 




Fig. 288. — Valve Gear of the Deane Pump. 1. Main Valve; 2. Auxiliary piston 
which moves main valve; 3. Auxiliary valve, with ports shown in views C and 
D; 4. Valve rod; 5. Slide block; 6. Rod to pendulum lever. 



(h) Steam-actuated Valves. — The underlying principle of all 
single steam pumps is well exemplified by Fig. 288. The external gear 
consists of an indirect pendulum lever, equivalent to rocker 2 in Fig. 
285, from which rod 6 (in view E) drives slide block 5. As the piston 
approaches the end of its stroke, block 5 strikes one of the tappets 



424 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



T, T, and moves valve 3. The latter, in form a hollow rectangle sur- 
rounding the main valve, serves two sets of little ports such as are 
diagrammed at C; through these steam is conducted to and from the 
cylinder spaces at the ends of the piston slide 2. Thus a small move- 
ment taken from the piston near the end of stroke sets into action 
what is really a complete secondary engine, which performs the function 
of moving the main valve. The reason for a double set of auxiliary 
ports is apparent when we note, in view C, that the steam port is car- 
ried clear to the end of the chamber, while the exhaust port is kept in 
from the head, so as to insure cushioning. 

All gears of this type have essentially the same elements, but in 
the form and arrangement of the secondary valve, ports, and gear there 
is wide variety. 

(i) Indicator Diagrams from Steam Pumps. — These engines all 
take steam through the full stroke, and when working against the 
nearly constant resistance of water give an indicator diagram which 






/ <-* N 










Up 


\ 
\ 
\ 

\ 

s 


IV. 


/ Down 










1 


i 
• 



Fig. 289. — Pressure Diagrams from the Air-brake Pump. 



approximates a rectangle — except as the reaction may be modified by 
the effect of inertia of a long column of water. When the resistance is 
not constant, but increases along the stroke as in the air-brake pump or 
in a condenser " air pump," the steam diagram takes the peculiar form 
at I in Fig. 289. Here I and II are corresponding indicator diagrams 
from steam end and air end, brought to the same scale of pressures. 
Considering simultaneous lines of forward pressure and back pressure 
in I, we see that a small driving force at first is obtained chiefly by 
throttling the exhaust; instead of taking place while the piston is at or 



§ 44 (i)J 



VARIOUS VALVE GEARS. 



425 



near the end of its stroke, the release (with drop in pressure) is distrib- 
uted along a good part of the return stroke. As the air resistance in- 
creases, the piston, which started off rapidly, slows down; and during 
the expulsion of the compressed air the two steam pressures are nearly 
constant at their maximum and minimum values. Diagrams of effec- 
tive driving force and effective resistance are plotted at III and IV, 
from I and II, respectively, to show how very closely the two force 
actions agree, there being between them only the small differences 
needed to accelerate the pistons. 

The necessary throttling action is secured in large degree by the 
use of very small ports : thus in the machine from which the diagrams 
in Fig. 289 were taken, the ratio of port area to piston area is about 
1 to 130, as against perhaps 1 to 10 in an ordinary engine. 

(j) The Self-centering Valve. — Fig. 290 is introduced with the 
purpose of illustrating a type of valve gear used in a wide variety of 




Fig. 290. — Reversing Gear for a Large Rolling-mill Engine. I. Operating cylinder, 
with steam; II. Brake and holding cylinder, with water or oil. 

regulating devices, in which the part moved or adjusted must follow a 
control lever or handle. We are not now concerned with the Stephen- 
son gear, pieces 1 to 7, but with the valve mechanism of the operating 
cylinder. The floating lever CDF is pivoted on the valve rod 13 at 
D. Suppose that hand lever 10 is swung to the left: CF will follow it, 
turning on F, and drawing the valves on rod 13 to the left. This will 
admit steam to drive the pistons to the right; and as 7 turns clock- 
wise, it will push lever FC to the right, at F, compensating for the 
original displacement by hand, and bringing the valves back to the 
closed and holding position. Thus the main link 2 takes always a 
position definitely related to that of the hand lever 10. This principle 
has many applications, and the mechanisms which embody it differ 
greatly in form and detail. 



426 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



§ 45. Steam-engine Governors 

(a) Functions of the Governor. — The two types of cut-off gov- 
ernors have already been described, as to general form and working and 
as to their control of valve action, the fly-ball governor in § 43 (d) , the 
shaft governor in § 2 (m) and § 39 (6). In a study of the forces which 
act within governors, two main questions come up, or two functions 
are to be considered. The first is the question of " regulation," or 
of the manner in which the speed in steady running varies with the 
load; the second is concerned with "adjustment," or with the behavior 
of the governor while in the act of accommodating the engine to a change 
of load: involved in both, and by no means of subsidiary importance, 
is the question whether the governor will hold steadily the position cor- 
responding to a constant load, without yielding unduly to the action of 
secondary disturbing forces. By " close regulation "■ is meant that the 
whole range of load is covered with only a small change in speed — 
this change being normally a decrease as the load increases. An ideal 
governor, while steady under constant load, would respond at once to 
any change in the main controlling forces, following the load to the 

new position of equilibrium and stopping there, 
without superfluous movement on its own 
account. To realize this ideal is by no means 
an easy problem. 

(b) Typical Force Action. — To establish 
certain fundamental concepts and principles, 
consider the simplified arrangement in Fig. 
291. The ball at the end of the arm pivoted 
at P can swing in the plane of the drawing, 
while this plane has a rotary motion about 
the axis AP. For equilibrium, centrifugal 
force F must balance gravity force W, or there must be an equation 

of moments, 

Fh = Wr (208) 




W W 

Fig. 291. — Element of 
the Fly-ball Governor. 



The force F is a function of the r.p.m. N, according to the relation 



W v 2 
F = —- = aWN 2 r, 
g r 



(209) 



where a is the resultant constant. Substituting in the first equation 
and getting a new constant, 



aWN*rh = Wr, and N 



-»vi 



(210) 



§ 45 (&)] STEAM-ENGINE GOVERNORS. 427 

This shows how the balancing speed varies with the position of the 
pendulum arm. 

The equilibrium represented by Eq. (208) is a perfectly general 
requirement: but the transformations which follow belong to the par- 
ticular case. If the pivot P is not on the axis of rotation of the gover- 
nor, the moment arm of W about P is not the same as the radius which 
determines centrifugal force: then the relations and their expressions 
will become less simple than in Eq. (210). 

(c) Stability. — To see how and why stability of position exists 
in a governor, return to Fig. 291 and suppose the rotation about the 
axis AP to be maintained at a constant speed N. If by some external 
force the ball is pulled down from its normal position, the moment of 
W, dependent upon r alone, will decrease more rapidly than that of 
F, which varies as the product rh; then the excess of the latter will 
swing the arm upward. With displacement on the other direction, r 
increases more rapidly than rh, and again there is an unbalanced 
moment acting toward the normal position. Roughly, with a constant 
speed, the force tending to return the ball to the neutral position is 
proportional to the displacement from that position. 

For a series of governor positions and at a constant speed N, let 
values of the moment (Fh) be calculated and compared with (Wr) ; as 
there is less difference in their manner of variation, less change of speed 
will be needed to establish a new balancing position: the governor will 
be more nearly isochronous (of constant speed) , but the stability against 
a disturbing force will be less. A perfectly isochronous centrifugal 
governor mechanism has no stability at all, and cannot be used to con- 
trol an engine. 

(d) Action in Adjustment. — When the speed of an engine changes 
under change of load, the equilibrium position of the governor is 
shifted. The resulting unbalanced force at once begins to produce 
motion in the mechanism, but the acceleration of the mass requires a 
certain amount of time. Generally, the governor comes to the new 
position with some velocity and momentum, and swings past until 
checked by the reversed balancing force, then swings back in the same 
way. The tendency is to set up a regular pendulum motion, until the 
energy of the initial impulse has been absorbed in friction or in some 
other brake action. The study of this phase of the performance of 
governors is one of the most complicated subjects in the Mechanics of 
Machinery, and nothing but the preceding brief outline is appropriate 
here. 

(e) Regulation by the Fly-ball Governor. — In Fig. 292 are 
outlined three typical forms of this governor, all weight-loaded, or with 



s 



428 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



gravity as the force that acts against the centrifugal force of the balls: 
sometimes the load is furnished partly by springs, especially in small 
throttling governors. The first example in Fig. 292 corresponds with 
Fig. 268; it is slow-running and largely self-balanced, the weight on the 
central slide being small in comparison with that of the balls them- 




Fig. 292. — Types of the Fly-ball Governor: I. Common Low-speed Governor; 
II. High-speed Governor, Weight-loaded; III. The Proell Type. 

selves. No. II runs at high rotary speed, hence the balls are small 
and most of the counterforce is furnished by the big central weight. 
No. Ill is a prominent German design: by placing the balls as shown, 
much closer regulation is secured than, for instance, in I. 




lit ii i i f i i i i I i i i i I i i i i — iiii|iiiiiiii i I i i i i I i i ii | i i 
>2 Ins. "i o ' l| ' l 2 

Fig. 293. — Curves of Regulation for Governor in Fig. 268. 

To show how the general relations in Art. (6) work out for a par- 
ticular case, results from the analysis of the governor in Fig. 268 are 
given in Fig. 293. The base of this diagram is the vertical path of a 
point on the central slide or sleeve, piece 6 in Fig. 268. The numbered 
ordinates correspond with a series of equally-spaced positions of the 
ball on its arc of travel; the ordinary range is from 2 (low) to 6 (high). 
By methods of kinematics, easy enough to apply but hardly appro- 



§ 45 (e)] 



STEAM-ENGINE GOVERNORS. 



429 



priate for description here, the forces of gravity on all the moving pieces 
of the governor, including the poise W, are reduced to the slide and 
there combined in the single resultant JFr. This tends to pull the gover- 
nor downward and varies, with position, as shown by curve I. Simi- 
larly, all centrifugal forces are reduced to equivalent lifting effects upon 
the slide and combined in F-&, which varies with both position and 
speed. Curve II gives Fr as worked out for the speed which gives 
equilibrium at position 4, or for 86.2 r.p.m. in this mechanism and 
with the poise at the middle of its arm: by moving the poise from one 
extreme to the other, the mid-position speed can be changed from 79 
to 93 r.p.m. of the governor. Comparing curves I 
and II, we see that to make i^R equal Wr, the 
speed must be lower at low positions, higher for 
the upper range. Curve III shows how N must 
vary for balance in the governor, representing the 
ratio of changing N to N± at mid-position. 

This governor is by no means a close regulator, 
the total variation from ordinate 2 (resting on 
stop ring) to ordinate 6 (highest running position) 
being about 15 per cent of the middle speed. Fig. 
294 shows one simple scheme for improving the 
action of such a governor : by putting the poise W on an inclined arm, 
its moment arm will be made to decrease as the slide rises, and thus 




Fig. 294. — Counter- 
poise on Inclined 
Arm. 




Fig. 295. — Force Action in the Shaft Governor. 



curve I in Fig. 293 will be brought a little nearer to the inclination 
of curve II. 

(/) Force Action in the Shaft Governor. — In Fig. 295, the axis 
of rotation is projected in the point O, and OA is a radius in the plane 
of the wheel, out to the pivot pin A on which the weight arm AG can 
turn. At I is represented equilibrium between centrifugal force F, 



430 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



with moment arm AB, and spring force S, with arm AC. At II is 
shown a force action which comes into play during adjustment : the wheel 
being given an angular acceleration about in the clockwise direction 




Fig. 296. — Buckeye Governor. 



Fig. 297. — Westinghouse Governor. 



the inertia of AG will tend to turn it outward about A, thus helping 
the unbalanced centrifugal force to bring the governor to its new posi- 





Fig. 298. — Robb-Armstrong Governor. Fig. 299. — Rites Governor. 

tion. Into the detail of this action, intended to be illustrated by 
some extra lines on the diagram, we shall not enter. 

(g) Types of Shaft Governor. — Figs. 296 and 297 show two of 



§ 45 (g)\ 



STEAM-ENGINE GOVERNORS. 



431 



the older governors, so arranged, in the relative position of weight 
and of arm pivot, that inertia can exert very little influence. Further, 
in having a practically symmetrical form with reference to the axis of 
the shaft, they are balanced against any possible disturbance by gravity 
force. Since the governor rotates in a vertical plane, the gravity pull 
on each mass constantly varies in relative direction; and while this 
force is comparatively small, its cyclical fluctuation tends in some 
degree to set up an oscillating motion. 

Figures 298 and 299 represent governors in which inertia as an active 
influence during adjustment is intentionally given a prominent place, 
although both depend upon centrifugal force to determine the regula- 
tion. In these designs comparatively little effort is made to secure 
gravity balance, experience having shown that at high speeds the effect 
of unbalance is very small. 

(h) Control of Regulation. — In order to control the running 
speed and its manner of variation with load, most governors permit 




Fig. 300. — Types of Spring Connection. 

change of the mass in the weight or ball, and change of spring tension; 
while some have provision for moving the point of spring connection, 
on the weight arm. Concerning the last matter, Fig. 300 shows dif- 
ferent types of spring action. In the first case, the spring keeps an 
almost constant lever arm about A; in the second the arm decreases as 
the spring is stretched, while in the third it increases. The adoption 
of a particular point of spring attachment is commonly a question of 
original design rather than of subsequent adjustment; if provided for, 
the latter will probably take the form of a change of length in the 
arm A J. 

To add mass to the governor weight will make the engine run 
slower, to tighten the spring will speed it up. A combined change may 
keep the average r.p.m. nearly the same, but will affect the regulation. 
A given spring has a certain scale, or ratio of applied force to deflection 
produced. In the movement of the governor over its range, there is a 
definite change in spring deflection, hence a fixed increment of tension. 
If the initial tension is high, the increment bears to it a smaller ratio 
than if it is low. We see then that to increase mass and tension to- 
gether will make the regulation closer, or the variation of speed less. 



432 



VALVE GEARS AND GOVERNORS. 



[Chap. VIII. 



In electrical service, it is quite usual to provide means for adjusting 
speed from the switchboard, so that units can readily be synchronized 
for parallel operation — the work being done by a little motor mounted 
on the governor. 

(i) The Throttling Governor. — The example in Fig. 301, 
in its mechanism for regulating speed, is a good representative of 




Fig. 301. — Gardner Governor for Air Compressor. 



throttling governors in general: beside this, there is an apparatus for 
shutting down the engine when the air pressure rises to a certain de- 
sired height, and either device can operate independently of the other. 
The main mechanism, consisting of pulley spindle 1, hollow governor 
spindle 2, and fly balls 3, 3, is self-evident. Through the rod 4 and 
the intermediate pieces 5 and 6, the valve 8 is pushed down when the 
balls fly out, throttling the steam. This valve, being of the piston 
rather than of the double-seated disc form, is perfectly balanced, so 
that the very light stem 7 is sufficient: and the crossbar below the 



§ 45 (i)] STEAM-ENGINE GOVERNORS. 433 

valve insures that it shall never fall so far as to admit steam when it 
is intended to be closed. Piece 5 is held against 4 by the first spring, 
acting through lever 9; similarly, 6 is held against 5 by lever 12, the 
springs both having a certain share in determining the running speed. 
From the top of 6 a small pin or spindle projects into a central hole in 
5, to keep these parts always in line. 

The pressure governor consists of the cylinder 18, receiving the air 
pressure at C, with the plunger 17 and the weighted lever 15 which is 
pivoted at D. When the pressure gets to the desired maximum and 
raises the weight arm, the knife edge on the upper end of 16 pushes 
against the outer end of lever 12 and closes the valve. The stop screw 
19 can be set so that steam will not be quite shut off by this action, for 
if the compressor is completely stopped, it may be in a position from 
which it will not start when steam is again admitted. 



CHAPTER IX 
ACTION OF THE STEAM IN THE TURBINE 

§ 46. Dynamics of Jet Action 

(a) Impulse Upon the Jet. — The method developed and applied 
in § 16, for calculating the velocity of the steam jet, passes over all inter- 
mediate details of the process of accelerating the steam mass, and uses 
simply the final, overall relation, that since the pound of steam has 
received a certain amount of pressure work it must have gained an equal 
amount of kinetic energy. 

In the formation of the jet, steam with a negligible velocity of ap- 
proach is given a very high velocity, by a driving force which acts upon 
the steam mass in one direction and exerts an equal and opposite reac- 
tion upon the nozzle or containing vessel. This force, viewed preferably 
as a reaction, might be found by determining the variant pressures on 
the confining surfaces and summing up their components in the direction 
of the nozzle axis. Such an operation would be very complicated, 
whether by calculation or by experiment; but there is, fortunately, a 
simple way of getting at an equivalent net result. 

Start with the fundamental dynamic relation, Force = Mass X 
Acceleration, or 

F = MA, (211) 

and multiply both sides of the equation by time t; then 

Ft = MAt = MV. ...... (212) 

That is, when a free force F acts upon a mass M through the time t, 
and generates the velocity V from an initial state of rest, the product 
of force by time equals the product of mass by velocity, which latter is 
called the momentum of the moving mass. For applying these prin- 
ciples to the conditions represented in Fig. 302, let the fully-formed jet 
at the cross plane AB have the velocity V (feet per second), the cross 
area a (square feet), and the specific weight w (pounds per cubic foot). 
The discharge per second will be W = waV pounds, and its mass 

434 



§ 46 (a)] DYNAMICS OF JET ACTION. 435 

M = W/g. Taking any time interval t, substitution in the general 
equation (212) gives 

Ft = waVt v = WtV (213) 

g g 

or 

F = ^ = wv 

g 9 

With a unit or one-pound-per-second jet, W = 1; then the actual 
diffused and variant pressure which produces the jet is equivalent to 
a single, concentrated force of the value 

F=- (215) 

9 

As represented in Fig. 302, this may be called the impulse upon the jet: 
upon the nozzle there must be an equal and opposite reaction. 

(6) Impulse and Reaction of the Jet. — In Fig. 303 a jet of steam 
is shown as flowing through a pipe or tube and impinging squarely upon 
a flat plate MN. The latter spreads the stream sidewise in all direc- 



1 k 



II. F M 



■* 



r 



Q±L 



»- 



J 



S3 



BO H 



n 



N 



Fig. 302. — Impulse upon Fig. 303. — Impulse Exerted 

the Jet. by the Jet. 



tions, destroying the velocity in the original direction of flow. The 
pressure on the plate MN, equal and opposite to the force F, in the 
figure, which is required to hold this in position, is the impulse of the jet. 
Figure 303 illustrates a derivation of the value of force F through 
work and energy relations, instead of momentum. The mass to be 
discharged in one second is shown as included between the planes CD 
and EH, which are separated by the distance V feet. At the beginning 
of the particular second under consideration, the plane EH just touches 
MN; and the center of mass G being then at the distance § V, this is 
the average distance through which the resistance F will act upon the 
mass W/g in bringing it to rest. Then equating work of retardation 
with kinetic energy lost, we have 

V wv 2 wv 

^X^=V-. F = — (216) 

2 2g g 



436 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Figure 304 shows the essential form of an apparatus which has been 
used in a number of experiments made to determine the reaction of a 
steam jet. The chamber represented by the square outline in I is at 
the lower end of an elastic tube, through which steam of high pressure 
has entrance. The steam blows out toward the right and tends to 
throw the box toward the left, exerting a reaction which can be measured 
by some weighing device or dynamometer. The arrangement is very 
effective as an illustration of jet action: but in its use for quantitative 
experiment there must be a clear understanding of the conditions exist- 
ing. Suppose, for instance, that with a flow from a high pressure p\ 
into a low pressure pi, a plain converging nozzle (or an orifice with 
rounded entrance) is used, as in the first sketch. At the mouth or out- 
let of the nozzle, the steam in the jet will have the pressure po = 0.58 pi 





Fig. 304. — Reaction of Jet Formation. 



and the velocity V produced by expansion from pi to p — note the 
representation at II, and refer to the remarks on this state of affairs 
in § 16 (h). Beside the dynamic reaction F , there will be then a static- 
pressure reaction in the same direction; because upon the area a on 
the right side of the vessel (the nozzle mouth) reacts the pressure p , 
while upon the equal area on the other side acts only p 2 . If the diverg- 
ing nozzle at III is so proportioned as just to reduce the pressure in the 
jet at its mouth to p%, all static pressures will be balanced and only the 
dynamic reaction will be measured. Note what is said in § 47 (/) 
concerning the case of excessive divergence of the nozzle. 

Example 42. — Steam initially dry-saturated flows from a pressure of 
120 lb. abs. into 15 lb. abs., through a short converging nozzle with a least area 
of 0.25 sq. in. Assuming ideal flow, as defined in § 16 (a), find the discharge 
per second, the dynamic reaction, and the total reaction that would come upon 
the dynamometer in an apparatus such as is partly outlined in Fig. 304. 

Take the pressure at the mouth of the nozzle or in the plane of the orifice 
to be p = 0.58 pi = 69.6 lb. From Table 7, page 118, the throat area of the 
unit jet from 120 lb. abs. is 0.5868 sq. in. ; then through 0.25 sq. in. the flow will 
be 0.25 ^ 0.5868 = 0.4261 lb. per sec. 



§ 46 (&)] 



DYNAMICS OF JET ACTION. 



437 



By Table 6 directly, the ideal velocity at p is 1474 ft. per sec. Substitution 
in Eq. (214) gives 

F = 0.4261 X 1474 =19531b 
32.15 

With a static pressure of 69.6 lb. in the steam at the plane of the orifice, there 
will be on the 0.25 sq. in. of outlet a force of 17.4 lb.: on the opposing 0.25 sq. in. 
at the other side of the box acts a force of 15 X 0.25 = 3.75 lb.: then the un- 
balanced steam pressure is 13.65 lb., which raises the total reaction to R = 19.53 
+ 13.65 = 33.18 lb. . 

Example 43. — With the conditions in the last problem, find the proper 
mouth area of a diverging nozzle, then get the velocity and the dynamic reaction 
with full expansion in the nozzle. 

With pi = 120, p 2 = 15, the pressure ratio is 0.125. From Table 6, the 
area ratio a/a is 2.072, so that the mouth area should be 0.25 X 2.072 = 0.518 
sq. in. To the area ratio 2.072 corresponds a diameter ratio of only V2.072 
= 1.44. 

Again by Table 6, the velocity is 2755; and this in Eq. (214), with W from 
the last problem, makes 

0.4261 X 2755 



F 



32.16 



== 36.50 lb. =R. 



(c) Deflection of the Jet. — In Fig. 305 a flowing jet or stream 
is depicted as entering at A and leaving at B a frictionless channel of 
"uniform curvature and cross section. The velocity remains constant 





Fig. 305. — Deflection of a Jet. 

in intensity, and the action involved in its continual deflection is that 
of simple transverse, centripetal acceleration, against which reacts the 
centrifugal force of the stream. 

The essential dimensions and symbols are as follows : 
, a = area of cross section of channel, equals b X c, the stream having the 
width b and the depth c; 



438 ACTION OF THE STEAM IN THE .TURBINE. [Chap. IX. 

R = radius of center line of stream; 
a = angle between any pair of radii; 

I = length measured along curved center line; 

v = specific volume of fluid in jet; 
w = weight per cubic unit = l/v; 
V = velocity of flow; 
A = acceleration; 

W = weight of fluid discharged per second; 
F = impulse of jet. 

Consider an element of the stream which is included between two 
radial planes at the angular distance da from each other: 

Length = Rda; volume = aRda; mass = = m. 

The centrifugal force of this element is mV 2 /R, or 

. waRda V 2 waV 2 7 ,-, , /«-.«% 

/c = v = da = Fda, .... (217) 

g R g 

the reaction F being substituted from Eq. (214). The important result 
.follows that the total pressure required to deflect a jet through an angle 
a (this pressure being distributed along the curved guiding surface, and 
found by integrating from to a as indicated at II) is equal to the 
impulse of the jet multiplied by the value of a in radian measure. 

The disappearance of R from the expression for / c in Eq. (217) 
shows that with a given jet, or with V, W, and a fixed, the total deflect- 
ing pressure, or the summed up reaction of the jet against the curved 
surface, is independent of the radius of curvature. With a certain 
angle a, to make R bigger will make the channel longer and the con- 
tained mass of steam greater, and this compensates for the inverse 
variation of unit force with R. 

In Fig. 305, let us take the outer surface of the element of volume 
to be cRda, disregarding the fact that the outer radius is really (R+i b) ; 
division into the force / c will give the unit centrifugal pressure 

wbcRda V 2 wb V 2 /n -,n\ 

Vc = ■ — ^ d=- d ( 218 ) 

gcRda R g R 

Example 44. — Using, directly or indirectly, values in the 0.40 line of 
Table 6, let a steam jet at 48 lb. abs. pressure, with the velocity 1891 ft. per sec. 
and the specific volume 8.33 cu. ft. flow in a channel 0.5 in. wide and 1 in. deep, 
having the mean radius 2 in. What is the impulse of the jet and what the unit 
centrifugal pressure on the guiding surface, assuming that no losses by friction, 
etc., need be considered? 






§ 46 (c)] 



DYNAMICS OF JET ACTION. 



439 



Here a = 0.5 sq. in. = 0.00347 sq. ft. 

0.00347 X 1891 



The rate of flow is W = 



8.33 



= 0.788 lb. per sec. 



™ . i • r, 0.788X1891 .aoiu 
The impulse is F = ^ttTa = 46.3 lb. 

oZ. JLO 

In Eq. (217), b, c, and R must be reduced to feet, so that 

w be Rda 12 V 2 wbcRdoc V 2 



fc = 



g 144 12 R 1440 R' 



(217') 



but to get p c per sq. in., area cRda is used without change; then Eq. (218) 

becomes 

wb V 2 

*°-mr g ii (218 '> 

For this problem, noting that w = 1/8.33, we have 

0.5 X 1891 X 1891 



Vc = 



8.33X144X32.16X2 



= 23.171b. per sq. in. 



Using the larger outer surface of the channel, with the radius 2\ instead of 2 in. 
changes this to 

23.2x^ = 20.61b. 
2.25 

Evidently, there will be a strong crowding of the stream against the guiding 
surface, with some consequent departure from the ideal, orderly flow which has 
thus far been assumed. 

(d) Action of Jet upon Vane. — In Fig. 306, let AB represent the 
full velocity V of the jet as delivered by the nozzle. This jet flows 
upon a vane or into a "bucket" CD, 
which has the velocity Vt- To get the 
relative velocity Vi of entrance, that of 
the nozzle relative to the vane, laid off 
at BC as Vt reversed, must be combined 
with V in the triangle ABC. 

The function of the curved vane CD, 
or of the channel between two successive 
vanes, is to change the direction of the 
steam current so that it escapes with 
the relative velocity V2, here equal to 
Vi and making the same angle with the line of bucket movement. The 
dynamic pressure of the steam upon the curved guide, due to the 
inertia with which the current resists transverse acceleration, is the 
driving force in the turbine. 

Combining with V2 the vane velocity Vt at EF, we get DF or Vq as 




Fig. 306. — Velocity Diagram. 



440 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



the absolute exit velocity of the steam. The decrease in kinetic jet 
energy which accompanies the drop from V to V is equal to the work 
done by the steam in driving the turbine wheel — except that a portion 
of this kinetic energy may have been wasted in friction and eddies, and 
be carried as a part of the heat content of the steam. 

(e) Driving Force on the Vane. — Knowing the centrifugal force 
exerted by the jet upon a curved vane surface, the next step is to find 
the resultant, in a certain direction, of this radial force distributed along 
the vane. The problem is illustrated in Fig. 307, where the tangential 
force Ft is the resultant sought, acting in the direction of motion of the 





Fig. 307. — Resolution of Centrifugal Fig. 308. — Combining the Impulses. 
Force. 

vane or bucket. Resolving any elementary force / c , we get the driving 
component f T = f c cos a, and the axial component / A = / c sin a, the 
latter being parallel to the axis in the usual type of axial-flow turbines. 
To get F T we make two integrations, one on each side of this resultant 
line. From Eq. (217) we have 

/ T = cosada; . (219) 

then, for the resultant force, 



COS ada + / COS ada J 



= i^ (sin on + sin 0:2), (220) 

F being the impulse of the jet, as appears from Eq. (214). 

For the resultant axial force Fa, a similar deduction gives 

F A = F (cos ai - cos a 2 ) ; (221) 

obviously, it is highly desirable that this force be made zero, since other- 
wise there would be a dynamic end thrust on the rotor. 

The form of Eq. (220) suggests at once the simple method set forth 
in Fig. 308. Considering the jet as exerting a positive impulse i^i at 






§ 46 (e)] 



DYNAMICS OF JET ACTION 



441 



entrance and a negative impulse or reaction F 2 at exit, we have only to 
combine these forces, or their rectangular components, to get Ft and 
Fa- Since impulse is proportional to velocity, this gives a very easy 
and convenient method for the solution of problems in force action on 
the vanes of a turbine. 

(/) Types of Vane Action. — The meaning of the terms impulse 
and reaction, as used to distinguish the manner of working of steam 
turbines, has been explained in a general way in § 4. The turbine 
elements shown at I in Figs. 309 and 310 are intended to illustrate a 
fuller definition. The velocity diagrams at II are made a little more 
compact than in Fig. 306, by omitting the vane profile and drawing T 2 
in sequence with V\. The various forces in the diagrams at III are 
parallel and proportional to the corresponding velocities. 




T T 

Fig. 309. — Driving by Impulse Only. FiG. 310. — Driving by Reaction Only. 

In Fig. 309, the half vanes are so formed that the steam leaves them 
in a direction perpendicular to the line of motion : then only the impulse 
at entrance is effective to produce driving force Ft, and the energy 
abstraction is very imperfect, as appears from the large residual velocity 
Vq. Another way of expressing this last condition is to say that the 
resultant F and the working force Ft are comparatively small because 
Fi and F 2 have such a large angle between them. Very evidently this 
type of element must be completed by making the vanes symmetrical 
with respect to the center line AB, thereby getting the well-known form 
shown in Figs. 16, 21, etc. In other words, what is called an impulse 
turbine really is driven equally by impulse and by reaction. 

But while the scheme outlined in Fig. 309 is not effective, that of 
Fig. 310 is entirely so. Receiving the steam normally (to the line of 
motion) with the velocity Vi, the reaction element accelerates it to V 2 



442 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



and discharges it at a wide angle from the normal. This leads to the 
force diagram III, where we see that the resultant F or Ft is large and 
is right along the line of movement. It appears then that while the 
" impulse" turbine must use reaction, the " reaction" turbine can get 
along without impulse. The real distinction lies in the fact that in one 
case velocity is generated wholly in the nozzles, in the other case in 
both fixed and moving vanes. The characteristic vane profiles shown 
in Figs. 311 and 313 result from this underlying difference. With a full 
understanding of what lies back of the terms, there can be no objection 
to the ordinary nomenclature : and a further distinction can be drawn 
in that the effective exit reaction in an impulse turbine is due wholly 
to deflection of the jet, while that in the reaction turbine is due to both 
deflection and linear acceleration. The dotted line F' in Fig. 310 III 
shows what the resultant would be with F 2 equal to F\. 

After the explanation just given, the actual impulse-element profiles 
and their diagrams of velocity and of force in Figs. 311 and 312 ought 
to be self-explanatory. Of the wheel with buckets formed in the rim, 



5& 





Fig. 311. — The Radial Vane, with 
Side Admission. 



Fig. 312. — Bucket in Rim of Wheel, 
with Tangential Admission. 



no examples have been given in Chapter I; fuller illustration will be 
found in Fig. 354. In Fig. 312 the plane of diagrams II and III is that 
of the lower, sectional view at I, or it is the plane, perpendicular to the 
axis, in which the wheel rotates. Then the velocity diagram doubles 
back on itself, because the projection of V 2 is simply V\ reversed. It 
is necessary, of course, that Vo approach the radial direction, since the 
steam must escape from the wheel in that direction. The forces F h 
F 2 , and F should really lie on the same line in their diagram, but are 
here separated for clearness of representation. Whereas with side ad- 
mission the resultant F is itself the driving force, the same thing as Ft, 
with tangential admission there is a non-effective component F-r, act- 
ing to cause pressure in the bearings, but which can easily be balanced by 
admitting steam to diametrically opposite parts of the wheel. 



§ 46 (/)] 



DYNAMICS OF JET ACTION. 



443 



The reaction vanes in Fig. 313 differ from the limiting form in Fig. 
310 in that they provide for a small effective impulse at entrance. Since 
it is always desirable that the peripheral velocity be no greater than is 
absolutely necessary, this T is usually made quite a little less than the 







Fig. 313. — Diagrams for the Reaction Turbine. 

projection of V, giving V\ the slant shown. Then the vane profiles are 
made to fit the velocity diagram, as in any case. 

(g) Work on the Vanes. — The effective dynamic driving force 
F (called Ft in the preceding discussion) acts upon vanes which have 
the velocity T; then the power, or rate of work performance, is 

P = FT ft. lb. per sec (222) 

We shall now apply to several typical cases the principle represented 
by this equation, still adhering to the primary assumption that there 
are no losses by friction or by other secondary actions. In the figures 
immediately following, the velocity diagrams (from which the impulsive 
forces may be directly determined) are changed to a rather more com- 
pact form, than that used heretofore. 

In Fig. 314, for instance, all the steam velocities are laid out from 
the point A as an origin: AB is the initial absolute velocity V, AC the 




Fig. 314. — Velocity Diagram for the Impulse Element. 

relative entrance velocity Vi) the exit velocity AD or Vi is Vi reversed 
symmetrically; and AE is the final absolute velocity, or V . For a 
discussion of work performance we are concerned, however, not with 
any total velocity V so much as with its component U in the direction 
of motion, or along T; the effective impulses at entrance and exit being 



444 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



proportional to the velocities Ui and U 2 , according to Eq. (214). With 
the relation 

V 2 = U 2 + A 2 , (223) 

and with the axial component A remaining constant throughout the 

successive transformations which take place, we see that changes in 

the kinetic energy of the steam current are represented and measured 

by changes in the value of U 2 . 

Now for the impulse turbine, as represented by Fig. 314, and with 

the several velocities as there designated, the fundamental expressions 

are 

Ui = U - T and U 2 = U h .... (224) 

the latter equation embodying the condition of symmetrical reversal, 

and being subject to modification in the actual case. The effective 

impulses are now 

W W 

Fl== lL Ul and f 2 = - U 2 , 

Q 9 



and the work rate is 



W W 

p = VL T (Ux + U 2 ) = 2 — (UT - T 2 ). 

Q 9 



(225) 



Examining this for the maximum value of P, in the usual manner, 

we get 

dP W 

°^ = 2 V ^{U-2T), ...... (226) 

which becomes zero when T = J U, thus proving the oft-stated prin- 
ciple that the velocity of the vanes should be one-half the effective 




D 'x E F C T 

Fig. 315. — Velocity Diagram for the Reaction Element. 

velocity of the steam jet for maximum efficiency. The greatest work 
rate is now 



W 1 1 W 



(227) 



or, as it should be, the full kinetic energy available in the weight W of 
steam that passes in one second. 

(h) Work in the Reaction Turbine. — From the similar repre- 






§ 46 (h)] 



DYNAMICS OF JET ACTION. 



445 



sentation of the velocities in a reaction-turbine element, in Fig. 315 
which corresponds with Fig. 313, we get the relations 

Ui=U-rT, U 2 = U, (228) 

the second implying similarity between fixed and moving vanes. Then 



and 



F 1 + F 2 =-(2U- T), 

g 

w 

P=—(2UT-T 2 ). 

g 



(229) 



This is greatest when U = T, in which case the effective driving force 
is wholly due to reaction, since U\ will be zero or the steam will enter 
the vanes at right angles to T, as in Fig. 310. The maximum value of 
P is now 



W 
Pm = -U 2 ; 

g 



(230) 



but here U 2 represents only half of the energy of one complete stage, 
since U is generated twice, first in the fixed vanes, again in the moving 
vanes. The total kinetic energy generated and absorbed is properly 
expressed by 

fic-s^Vfl*), (231) 

* g 

this (2 U 2 ) being equivalent to the U 2 in Eq. (227). 

The relations just deduced by mathematical reasoning call for 
fuller explanation. As implied, the stage embraces two 
rows of vanes, one fixed, the other moving. The func- 
tion of the fixed element is to give to the steam the 
velocity and the kinetic energy which it must have if it 
is simply to move with the other element; then follows 
the question of change of motion within and relative to 
the moving element. This separation of the whole pres- 
sure drop and velocity generation into two parts is an im- 
portant and essential feature of the turbine. In contrast 
with it consider the reaction " wheel," reproduced from 
Fig. 17 as Fig. 316. Within the hollow arm and at en- 
trance to the nozzle, the steam mass has the kinetic energy jr IG 3^ 

due to the velocity T of the nozzle, and is at the full Outline of 
. .,. , , , . , 1 x t i the Reaction 

initial pressure pi (plus an increment due to centnlugal wheel. 

force) . The pressure drop generates a relative velocity V, 

and the residual velocity of the steam after discharge is V Q = (V — T). 

This residual velocity cannot possibly be reduced to zero: for (with 




446 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 

M representing the mass of steam discharged per second) reaction 
F = MV and work rate P = MVT; then to make T = V would make 
P = MV 2 , whereas the whole available energy of the jet is only 
W= %MV 2 . A closer analysis would show how the acceleration of the 
steam within the arm, as it flows outward, absorbs work. But with- 
out going into detail, we have the outstanding principle that if all 
of the pressure drop in a stage is reserved to the moving element, it 
will give to the steam a higher (relative) velocity than the (moving) 
nozzle is capable of assuming; hence there must be a considerable 
residual velocity, and even without secondary losses the turbine cannot 
reach unit efficiency in energy absorption. 

It is of interest to note that, for a stage of given value, the vanes 
in a reaction turbine must move faster than in an impulse turbine. 
With a single expansion, the energy available will produce the effective 
velocity Ui, and the best speed of impulse vanes will be J U\. In each 
of the two half-expansions of a reaction stage, the velocity generated 
will be £/r= 0.707 Ui, but the best speed is now this full Ur. In 
application, the reaction turbine has always a larger number of stages 
for a given range of pressure. 

Example 45. — In Fig. 314, let the angle a. be 20°, so that sin a = 0.342, 
cos a = 0.940. Making no allowance for secondary losses, calculate the veloci- 
ties, forces, and work quantities in an expansion stage from pi = 120 lb. to 
p 2 = 72 lb. abs., with one pound per second of initially dry steam and with 

From Table 6, with R p = 0.60, energy E = 40.80 B.t.u. or 31,740 ft. lb., 
and velocity V = 1429 ft. per sec. : then U = V cos a = 1343, T = 0.375 X 1343 
= 503, and A = V sin a = 488 ft. per sec. Assuming Vi = V 2 and component 
A constant, as in Fig. 314, the driving force of this unit jet upon the vanes is 

F = 2(U-T) 5j7 = 5221b- 
9 4 g 

Acting on vanes which move with the velocity T = 503 ft. per sec, this 
force does work at the rate 

P = 52.2 X 503 = 26,260 ft. lb. per sec, 
equivalent to 26,260 ■*■ 550 = 47.8 horse-power. 

With the given values of U and T, the residual component U = £ U = 336 
ft. per sec Then 

Vo 2 = A 2 + Uo 2 = 238,100 + 112,900 = 351,000; 

and division by 2 g reduces this (still for the one-pound-per-second jet) to the 
residual kinetic energy, 

E = 354,000 ^ 64.32 = 5457 ft. lb. 

By direct subtraction of P from E, 

E = 31,740 - 26,260 = 5480 ft. lb. 



§ 46 (h)] 



DYNAMICS OF JET ACTION. 



447 



Insufficient precision in the velocity values will account for the small dis- 
crepancy. 

The efficiency of the turbine wheel in absorbing energy, under the assumed 
ideal conditions, would be 

P __ 26,260 _ „ 

Actually, the efficiency of this high-pressure stage, measured in terms of net 
work deliverable by the turbine shaft relative to steam energy E, would probably 
lie below 0.50. 

(i) Variation in Running Speed. — It will be noted that neither 
Fig. 314 nor Fig. 315 is drawn for the case of ideal maximum efficiency, 
but rather for the conditions likely to be found in practice, where the 
vane speed T is made as low as is consistent with reasonably good work- 
ing. To see the effect of thus lowering T from the ideal value, we discuss 
Eqs. (225) and (229) as follows: 

For the impulse turbine For the reaction turbine 



W 
P = 2— (U 

g 



T)T; 



W 

P = — (2U 

g 



T)T. 



In both cases, let T = nU, and put the expression into the form, kinetic 
energy X a function, of n; this gives 



P = (^jU^(l-n)4n; P = (^ (7 2 ) (2 - n) n. 



(232) 



wi=0 


0.05 


0.1 


0.15 


0.2 


0.25 


0.3 


0.35 


0.4 


0.45 


n 2 =0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


= 1712 = 


0.19 


0.36 


0.51 


0.64 


0.75 


0.84 


0.91 


0.96 


0.99 



For the first case, let mi = 4 n\ (1 — rii), and evaluate for T varying by 

twentieths from zero to \ U; for the second, let m 2 = n 2 (2 — n 2 ), and 

go by tenths from zero to U. The common results are given in the 

tabulation below, and it is evident that the vane velocity T may be 

lowered to 70 or 75 per cent of the ideal value without serious loss of 

effect. 

0.5 
1.0 
1.0 

An important assumption underlying this table is that the vanes 
be changed in form, with the running speed, so as to get full effect 
from the conditions existing in any case: and this leads to the next 
matter to be taken up. 

(j) Vane Form and Speed Change. — The proper function of a 
set of curved vanes or guides in a turbine is, to receive a current of steam 
without shock, to change its direction without the formation of eddies, 
and to discharge it in a desired direction. The simplest question in- 
volved in the performance of this function will now be considered. 

The elementary problem of accommodating the shape of the vane 



448 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



to a proposed velocity diagram, is illustrated by Fig. 317. In Case I 
the conditions are those for maximum efficiency in an impulse turbine, 
the vane velocity T being half of the effective entrance velocity U: the 
concave profiles are arcs of circles, made tangent to the lines of direction 
of the relative velocities Vi and F 2 ; the convex profile is made up of a 
smaller arc and two tangents. If the channel between two vanes is to 




Fig. 317. — Vanes to Fit Various Speeds. 



have an approximately constant width, the vane must, of course, be 
thickened toward the middle — see Fig. 319. This effect is much 
exaggerated at II, where the vanes are proportioned so as to receive* 
and symmetrically reverse the full entrance velocity, when T = or 
the vanes are standing still. Case III is at the other limit, when T = U 
and the current simply flows between straight vanes, without exerting 
any driving force — this being the greatest speed at which the turbine 
could possibly be made to run by steam action upon symmetrical vanes. 
Change in the vane speed T, after the form of the vane has been fixed, 
is discussed in § 48 (i). 

(k) Channel Form and Area of Cross Section. — In the most 
usual type of turbine, that with axial flow and having vanes with side 
admission, the channels for the passage of steam all lie within an annular 
space, which changes in diameter and in radial depth according to the 
requirement for effective area. The steam current has, at any critical 
point, an actual velocity V n and a progressive component velocity A 
(see Figs. 314, 315, etc.) : the latter is parallel to the axis or normal to 
the line of vane movement, but the total velocity, as also the direction 
of the channel, is oblique to these rectangular reference lines. 

To understand the effect of this obliquity, consider Fig. 318, where 
the vanes in the rotor R are made straight, continuing the slant which 
actual vanes would have at entrance — being fitted, of course, to the 
velocity diagram II. Letting 6 represent the pitch of the vanes or the 
width of the channel in the circumferential direction, we see that the 
effective width is much less, having the value 

b = b sin a or 6i = 6 sinai: . . . . (233) 



§ 46 (k)] 



DYNAMICS OF JET ACTION. 



449 



in other words, making the walls helical decreases the width of the 
channel by an amount which increases with the inclination from the 
axial direction. 

In the turbine, the relation between the steam velocities, as shown 
at II in Fig. 318, is the same as that between the channel widths (in 
inverse order) for 

V = -J- and Vi = -^— (234) 

sin a smai 

Consequently the flow capacities are the same, since 

Vb = 7i6i = Ab . (235) 

-b - 





ho. 318. — The Oblique Channel. 



Fig. 319. — Channel of Constant Width. 



The last expression, Ab , is then the criterion by which to measure the 
effective area for the passage of steam. 

The preceding discussion determines relations which in the actual 
case exist at entrance to and exit 
from the channels between curved 
vanes. For the body of such a 
channel the conditions which give 
constant width are set forth in Fig. 
319, where the curved portion of the 
passage is included between the radial 
lines CA and CB, the same center C 
being used for the arcs through D 
and E. The straight lines (tangents) 
which form a large part of the outer 
profile of the vane section have, of 
course, the inclination of the velocity V\ as in Fig. 318, making the 
angle ai with the line CD. 

An interesting conclusion from Eq. (235) is that if in an arrangement 
like Fig. 320 the vanes are brought to a sharp edge and formed as in 
Fig. 319, the diminution of obliquity will compensate for the diminution 




Fig. 320. — Element of Curtis Turbine. 



450 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



of velocity due to abstraction of energy — this on the assumption that 
the velocity changes are according to a diagram like Fig. 322, where A 
remains constant. Only for the purpose of accommodating extra losses 
of progressive velocity, as by friction and eddies, need the channels be 
increased in radial depth within the pressure stage. 

(I) Action in the Multiple-impulse Turbine. — Taking Fig. 320 
as a typical example, we have its velocity diagram in Fig. 321, laid out 




Fig. 321. — Multiple-step Velocity Diagram. 

with the triangles in sequence, and showing how the bucket profiles 
are fitted to the lines of velocity direction. For the discussion of work 
relations, the single-pole diagram in Fig. 322 is preferable. Here the 
relative velocities of entrance and of exit are marked by the numbers 
1, 2, and 3 for each set of vanes. Following the method of Art. (</), 




Fig. 322. — Velocity Diagram for a Three-impulse Stage. 

and dropping for the time the factor W/g in Eq. (214), we have the 
following expressions for the driving forces in the respective stages: 

F 1 = 2(U - T);F 2 = 2 (V - 3 T); F 3 = 2 (U - 5 T). (236) 

Of course, the velocity factor T in P n = F n T is the same all through, 
so that the work rates are proportional to the impulsive forces. If, for 
instance, T is one-seventh of U, as in the figure, the quantities of work 
done by the steam upon the vanes are as 6, 4, and 2 in the three velocity 

stages. 



§ 46 (I)] DYNAMICS OF JET ACTION. 451 

To show the identity, under the conditions of simple theory, of the 
above example with the equivalent single-impulse element, we first add 
the three driving forces in Eq. (236), then multiply by T to get the power 
developed, the results being 

F = 6 (U - 3 T); P = 2 (U - 3 T) X 3 T. 

Since a single-impulse stage with the same limits V and V as in Fig. 322 
would have the vane speed T r = 3 T, the desired equivalence is self- 
evident. 

(m) Path of the Jet. — The absolute path of an element of the 
steam current, as it passes along the moving vane, is a matter of interest; 
and, in cases like Figs. 365 and 354 III and IV, is of considerable practical 
importance. Plotting this path is a simple geometrical process, which 
is shown in Fig. 323 for the side-admission vane. 

First of all, the vane profile ABC is divided into, say, eight equal 
parts; then, from either velocity triangle, the distance that the vane 
will move on account of T while the 
steam travels over one interval with 
the velocity Vi or F 2 is found. This 
is laid off parallel to BD, the proper 
number of times from each numbered 
point on ABC, and the result is the 
path ADE, which is tangent to V and 
V at A and E respectively. For a 
tangential bucket, as in Fig. 354, the 
method would be essentially the same. 

In the reaction turbine it would be Fig. 323. — Plotting the Path of the 

bteam Current, 
necessary to know how the steam is 

accelerated within the bucket ; but with full peripheral admission there 

is no need of this determination. 

(n) Absolute Velocity in the Vane Channel. — For the vane 
profile drawn in Fig. 323 and with the initial and terminal velocities 
there shown, the variant absolute velocity of the flowing steam is deter- 
mined in Fig. 324. The vane velocity T is first laid out as AB, then 
from B is struck an arc with the radius V\ or T 2 : the length of this 
radius represents the uniform relative velocity assumed to exist along 
the channel, while successive angular positions show the direction of 
that velocity at the successive numbered points along the curve in 
Fig. 323. After putting in Vi and V 2 and dividing the arc C8, we draw 
vectors from A to the points on this curve, and thus get a series of 
absolute velocities, referred to the fixed body of the machine. 

At II, on a base which represents the vane profile when " developed," 




452 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



the steam velocities are laid out as parallel ordinates. The kinetic 
energy of an element of the current varies as the square of this ordinate, 
and thus can be seen how the initial energy is gradually diminished as 





Fig. 324. — Determination of Absolute Steam Velocity. 

the advancing jet performs work upon the moving vane. The experi- 
mental observations of pressure described in § 47 (n) indicate that this 
smooth and simple transformation of energy falls far short of realization. 



§ 47. Experiments on the Steam Jet 

(a) Flow Through Orifices. — A large number of experiments 
have been made to determine the rate of flow of steam through orifices 
and nozzles. The various results are generally quite consistent, and 
are put into the most useful form when brought into comparison with 
the calculated flow under ideal conditions, so that coefficients of dis- 
charge can be found. Several typical and representative sets of flow 
tests will now be given, and others will follow in the account of experi- 
ments where the rate of flow was not the principal determination. For 
calculating the ideal rate, Tables 6 and 7 are used, with the relations 
and methods of § 16. 

Table 17. Peabody Experiments 



Set. 


Length, 
inches. 


Pi p« 

Vl ¥t n 


w 


D T W T 


c 


A 
B 
C 
D 


1.5 
0.5 
0.25 
0.25 


88.0 0.33-0.45 0.634 
87.5 0.34-0.51 0.616 

87.1 0.34-0.45 0.583 
140.4 0.30-0.40 0.596 


0.0606 
0.0623 
0.0627 
0.0992 


69.80 0.0617 
69.80 0.0615 
69.79 0.0613 
70.70 0.0974 


0.918 
1.013 
1.023 
1.019 



C. H. Peabody, Trans. A.S.M.E., 1890, Vol. 11, 187-192. 

In the experiments of Table 17, the steam flowed through what 
was really a short, straight nozzle: the rounded entrance had a quadrant 
arc of about 1 in. radius for profile, while the tubular part was 0.25 in. 



§ 47 (a)] EXPERIMENTS ON THE STEAM JET. 453 

in diameter and had the three lengths given in the first column of the 
table. At mid-length of the cylindrical portion of the nozzle, a small 
hole was drilled in from the side, and connection was made to a gage 
which showed the actual "throat" pressure p . The four lines in the 
table are means of groups containing two to five individual tests. The 
only quantity that had more than incidental variation within the group 
was the low-side pressure p 2 , and this is covered by giving the range of 
the ratio P2/P1', in all cases, p<i was well below the critical value 0.58 p\. 
Before considering the calculation of ideal flow, best illustrated by an 
example, note how well the observed pressure in the tube conforms to 
the theoretical throat pressure : naturally, it would be higher as the tube 
was longer and the gage hole farther from the outlet. 

Example 46. — For line C of Table 17, take from Table 7 the value 69.79 
for the Napier divisor D. This corresponds, of course, with the normal or 
ideal throat pressure p = 0.58 pi. The area of a 0.25 in. circle is 0.04909 sq. in. 
Then the theoretical flow per second is 

Wt _g,_ 0.04909 X 87.1 = 006131b (23y) 

Dt o9.79 

The measured flow W being 0.0627 lb. per sec, the coefficient of discharge is 

W _ 0.0627 _ 
C ~ Wi " 00613 " im6 (238) 

(6) The Rateau Experiments, represented by Table 18 and plotted 
in Fig. 326, constitute perhaps the best single body of data on the flow 
of steam through the convergent nozzle and the plain orifice. Out of 
about 150 results, selected examples are given in the table, while the 
nearly 100 points in the diagram show the whole set, since many of 
these points stand for two or more practically coincident values. The 
nozzles tested are given in Fig. 325, with orifice diameters and with 
areas in square inches marked on the drawing. The columns in the 
table are as follows: 

pi = initial pressure in pounds per square inch absolute j 

R p = ratio of discharge or low-side pressure pi to p h or is pi/pi', 

Dt = theoretical Napier divisor, from Tables 7 and 6., to be used in 

Eq. (237); see Example 47; 
Wt = theoretical flow in pounds per second, by Eq. (237); 
W = actual flow, in same terms as Wt', 
c = coefficient of discharge, by Eq. (238). 

When p 2 does not exceed p or 0.58 p h Dt is taken directly from 
Table 7, for the particular value of pi. If pi is above p , this D must 
be enlarged, using the area ratio a/a from Table 6. As a increases, 






454 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Table 18. Examples from Rateau's 
Experiments on Flow of Steam 



Set. 


Pi 


Rp 


D T 


W T 


W 


c 




151.9 


0.890 


103.9 


0.1559 


0.1494 


0.959 


A 


143.7 


0.738 


76.19 


0.2008 


0.1965 


0.979 


151.4 


0.466 


70.84 


0.2280 


0.2305 


1.011 




138.3 


0.015 


70.67 


0.2083 


0.2124 


1.020 




77.1 


0.953 


149.5 


0.1453 


0.1370 


0.941 




86.2 


0.908 


110.4 


0.2200 


0.2100 


0.955 


B 


55.7 


0.891 


101.36 


0.1550 


0.1474 


0.951 


58.3 


0.474 


68.96 


0.2382 


0.2417 


1.013 




58.8 


0.282 


68.98 


0.2406 


0.2446 


1.016 




110.7 


0.019 


70.27 


0.4038 


0.4130 


1.022 




57.4 


0.984 


248.0 


0.1770 


0.1587 


0.895 




57.6 


0.951 


145.9 


0.3022 


0.2760 


0.913 




17.6 


0.864 


89.36 


0.1507 


0.1404 


0.932 




22.5 


0.782 


75.92 


0.2266 


0.2170 


0.957 


C 


21.4 


0.687 


69.54 


0.2354 


0.2321 


0.987 




23.2 


0.544 


67.02 


0.2647 


0.2642 


0.998 




22.8 


0.432 


66.98 


0.2600 


0.2628 


1.011 




16.9 


0.105 


66.32 


0.1951 


0.1980 


1.015 




41.7 


0.058 


68.25 


0.4680 


0.4720 


1.010 




70.9 


0.965 


171.3 


0.2048 


0.1273 


0.622 




46.0 


0.838 


85.97 


0.2650 


0.1775 


0.670 


D 


41.4 


0.640 


68.91 


0.2977 


0.2227 


0.749 


58.8 


0.396 


68.98 


0.4218 


0.3555 


0.843 




54.9 


0.257 


68.84 


0.3943 


0.3473 


0.881 




57.5 


0.039 


68.93 


0.4130 


0.3642 


0.883 




D V 



.792'M -495 D 1 



Fig. 325.— Nozzles Used 
in Rateau's Experi- 
ments. 



A. Rateau, Experiments on the Flow of Steam through Nozzle3. Pub- 
lished (book form in English) in 1900. Experiments made in 1896. 

running up the jet from a , in exactly the same way must D increase if 
Eq. (237) is to be used at any cross plane. 

The ordinate in Fig. 326 is the coefficient c, on the ratio R p as base. 
Curves A, B, C (for the similarly designated nozzles) are separated, 
each having its own scale, while N is their average to the main scale 
at the left, which serves for curve D also. Except at the beginning of 
curve C the results are smooth and consistent, even with irregularities 
greatly magnified by the coarseness of the vertical scale. Variation 
in the initial pressure p h as distinct from variation in R p , seems to have 
very little effect. For the converging nozzle, actual flow conforms to 
ideal when p 2 — Po, but the coefficient c drops off toward 0.9 as p 2 
approaches pi, and runs above unity when p 2 becomes small. This 
excess flow with low discharge pressure has not been rationalized, but 
is amply confirmed by other experiments; further examples, of flow 
through diverging nozzles, will be found in Art. (d). It does not appear 



§ 47 (6)3 



EXPERIMENTS ON THE STEAM JET. 



455 



that the small differences of form in nozzles A, B, and C have any 
effect upon rate of flow. 

With the plain orifice D, flow is relatively smaller, because of con- 
traction of the jet: but the discharge continues to increase quite rapidly 



IXDO- 




Fig. 326. — The Coefficient of Discharge, as Calculated from Rateau's Experiments. 

as p 2 falls below p , showing that the influence of contraction is largely 
dependent upon the density of the medium into which discharge takes 
place: this action of a thin-plate orifice is, however, in decided contrast 
with that of tubular orifice A in Fig. 328. 

Example 47. — In the first line of Table 18, with p x = 151.9 lb. abs., D 
from Table 7 is 70.84. With R p = 0.890, the value of. a/a from Table 6 is 
1.466. Multiplying, 

D T = 70.84 X 1.466 = 103.85. 

With the orifice area 0.1066 sq. in., the calculated flow is 
0.1066 X 151.9 



W T = 



103.9 



= 0.1559 lb. per sec. 



(c) Flow of Superheated Steam. — In Fig. 327 are plotted the 
results of some large-scale determinations of the flow of superheated 
steam: the rate was from 8000 to 9000 lb. per hour, the orifice being 
used to " waste" steam in some special boiler tests. The pressure was 
160 lb. abs. for the- series given, and efflux was into the atmosphere. 



456 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



The diagram is plotted on degrees fahrenheit of superheat as base. 
The curve marked Z>t shows the calculated Napier divisor, worked out 
for p = 0.58 pi, as in Example 48, following: it is extended to 300 deg. 
in the upper right-hand part of the drawing. Corresponding with Dt, 
Wt is the theoretical flow in pounds per second; and the dotted lines 



200 Dec 

821" 




Fig. 327. — Flow of Superheated Steam into Atmosphere, from 160 lb. abs., through 
1.2 in. orifice. Tests reported by I. Harter, Jr., Jour. A. S. M. E., Dec, 1910, 
Vol. 32, 2017-2021. 

are at 1, 2, and 3 per cent below the full unit value of this quantity. Ex- 
perimental flow results having been plotted as W points, coefficients of 
discharge can be read on the scale furnished by these dotted percentage 
lines. 

At first sight, the fact that this coefficient lies below unity seems to 
contradict the showing of the last article; but when we note how small 
is the radius of rounding at entrance to the orifice, a ready explanation 
suggests itself in the very probable existence of some contraction of the 
jet. Why the ratio of discharge should decrease with greater superheat 
is not apparent. 

Example 48. — Calculate theoretical conditions at 200 deg. of superheat 
for Fig. 327. 

Initial pressure p x = 160 lb. abs. 

Saturation temperature t sx — 363.6 deg. 

Initial steam temperature t x = 563.6 " 

By Table VIII, at p x and t x , entropy n x = ... 1.6846 

Throat pressure p = 0.58 p x = 92.8 lb. 

By Table VIII, at n x and p , temperature t = . . 439.5 deg. 

By Table VII, at p x and t h total heat hi = ... 1304.5 B.t.u. 

By same table, at p and t , total heat h = . . . 1248.0 " 

Then available energy E = h x — h = 56.5 " 



§ 47 (c)] 



EXPERIMENTS ON THE STEAM JET. 



457 



By Eq. (104), steam velocity V = 223.7 VE = . . 1679 ft. per sec. 

By the method of § 12 (i), Example 2, 

at p and t , specific volume v Q = 5.637 cu. ft. 

™ 144 v 144x5.637 n AQO 

Then area a = — = — = — — = 0.483 sq. m. 

V o lo79 

And D T = pido = 77.4 

The area of a 1.2 in. circle is . . . 1.131 sq. in. 

Whence the ideal flow per second is 

1.131 X 160 



W T = 



77.4 



2.34 lb. 



The circle-marked points along the Dt curve in Fig. 327 are from 
calculations like the preceding. Their erratic departures from a smooth 
curve are due in part to the impossibility of making very precise read- 
ings in the table-diagrams for superheated steam, in part to insufficiently 
consistent spacing of the curves in these Tables VII and VIII. An 
error of 0.5 to 0.7 B.t.u. in the value of the available energy E is enough 




140 120 P 2 100 LB. 80 AB3. 60 40 



Fig. 328. — Selected Results from Experiments by Gutermuth, Zeitschrift des 
Vereines deutscher Ingenieure, 1904, Vol. 481, 75-84. Steam dry-saturated. 

to cause the discrepancies which appear at 100 and 150 deg. This 
calculation is an exceedingly severe test of the accurate interrelation 
of the diagrammed properties of superheated steam. 

(d) Flow Through Divergent Nozzles. — Experiments made 
simply to determine the rate of flow are well represented by the results 
set forth in Fig. 328. The flow pieces are shown at the left of the 
drawing, all having a least diameter of 5.4 mm. or 0.213 in. Each series 



458 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



is for a constant initial pressure, here 3, 6, and 9 atmospheres respec- 
tively, or 44.1, 88.2, and 132.3 lb. per sq. in. The discharge pressure 
pi was varied over a wide range, and is the determining abscissa in the 
diagram. Plotted points show experimental data, while the curves 
represent calculated flow, with assumed adiabatic expansion, or the 
regular " ideal" action. On each curve a cross line is drawn at T to 
mark the throat pressure p , another at M to show the muzzle pressure 
of nozzle C*: the latter has about the area ratio a 2 /a = 2.05, for which 
the pressure ratio is R p = 0.133, by Table 6. 

Square-shouldered orifice tube A naturally shows a big falling off 
from ideal flow, but differs from the thin-plate orifice of Rateau, Fig. 326, 
in that the flow does not continue to increase after p 2 falls below po. 
Orifice B keeps very close to ideal discharge. The most striking thing 
shown, however, is the way in which points from nozzle C lie far above 
the calculated curve for values of p 2 higher than p Q , so that the nozzle 
reaches full discharge with p 2 as great as 0.8 p\. These experiments 





100 


p. 




115 


Lb.Abs. 






30 






1 


45 


















. Nozzle - 






























* 








* 


























n 






























* 


y 








* 
























































1 C\ 
































IU 
























































» 








1 1 
















* 
















1 1 






















































































































1 








" 


12 






* 








* 


















































































■ 18 






















































* 










13 






* 


















































' H 








































\A 
































•^ 
























J 1 
























* 
















































































15 
































































• \c 




















1 




1 1 




r 




• lb 

1 1 








l l 








J 



QIO 



0.11 W 0.12 LB. 0.13 Per 0.14 Sec. 0.15 



0.16 



Fig. 329. — Rates of Flow, Tests of Steam-turbine Nozzles, Sibley and Kemble, 
Trans. A. S. M. E., 1909, Vol. 31, 617-653. Nozzles in Fig. 330, discharge into 
vacuum. 

have been cited more to exhibit this phenomenon than because of any 
especial quantitative value which they possess for present purposes: 
but before the matter of overexpansioh in the nozzle is taken up, the 
further flow tests in Fig. 329 will be considered. 

In these Sibley and Kemble tests, which deserve decided prominence 

* That is, the pressure to which the steam will be expanded when the ideal jet 
has the same degree of divergence as that of this nozzle. 



§ 47 (d)] 



EXPERIMENTS ON THE STEAM JET. 



459 



and will be more fully discussed presently, the four initial pressures 
marked along the top of Fig. 329 were used, and the points grouped 
beneath each value represent tests at (or from) that pressure. The 
abscissa of the diagram is, of course, the rate of flow, in pounds per 
second to the scale at the bottom. At the left of each group, a heavy 
vertical line shows the calculated ideal flow, with steam initially dry- 
saturated and with an orifice area of 0.0725 sq. in. — all measured rates 
being reduced to this prevailing area. To the right of each ideal line 
are drawn five percentage lines, at intervals representing one per cent 
of the ideal flow; then coefficients of discharge can be read off directly. 
The short vertical lines across sets 11 and 14 will be referred to from 
Art. (k). The vertical spacing has no quantitative meaning, but each 
horizontal line ties together the tests made on a certain date. For the 
present we note simply that the coefficient of discharge ranges from 
1.02 to 1.05. 

In Fig. 330, beside the length and angle of divergence, each nozzle 
profile carries three numbers; these are: beneath the throat, the throat 



9B 




o 1.593 

Ci h 

* 21.8 




.0125 



Fig. 330. — Nozzles tested by Sibley and Kemble. 



area a in square inches; near the muzzle, first the mouth area a 2 , then 
the area ratio a 2 /«o. All the nozzles were of machinery steel, bored 
smooth and polished; except that No. 18, otherwise like 11, was left 
with a fine tool mark, which, however, does not appear to have had any 
effect upon rate of flow. Nozzle 15 was round in approach and throat, 
but was made in halves and milled out to a square muzzle. Nos. 9 and 
13 are search-tube nozzles, and No. 12 has an unusually wide cone angle. 



460 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 





Fig. 331. — Nozzle with Search 
Tube; overexpansion shown. 



(e) Measurements of Pressure in the Jet. — From the begin- 
ning of definite investigation of the steam jet, the variant pressure within 
the steam current has been one of the important quantities measured; 
and a search tube lying in the axis of the nozzle as outlined in Fig. 331, 
is the best and most used device for this purpose. One or more holes 
are drilled through the tube at a particular point in its length : one end 

is closed, the other goes out through a 
stuffing box and is connected to a 
pressure gage. The tube can be moved 
lengthwise, and an external measuring 
arrangement determines the position 
of the holes along the nozzle axis, 
usually referred to the cross plane of 
the throat as datum position. 

Paralleling the scheme of the search 
tube, we have that of drilling holes 
through the sides of the nozzle, already 
described, in limited application, in 
connection with Table 17, Art. (a). 
This method lacks flexibility in change 
of locus, and calls for complex gage 
connections. With a straight-line profile (in a cylindrical or conical 
tube), so that no curvature of path evokes transverse inertia of the 
stream elements, only an accidental condition will cause any difference 
between pressure measurements at the axis and at the envelope of the 
jet; so long as orderly flow is maintained, it is immaterial where the 
pressure is taken, in a given cross plane. 

In Stodola's Steam Turbines will be found an account of some com- 
parative pressure measurements, made with holes in the sides of search 
tubes drilled obliquely (at 45° slant), some inclined against, some with 
the current. The observed pressures differed in very uniform fashion, 
and their mean was just about equal to the reading with holes drilled 
perpendicular to the surface. That the latter arrangement gives essen- 
tially correct results is the conclusion announced. 

(/) Curves oe Pressure Variation. — The diagram below the 
nozzle in Fig. 331 shows first, in the curve AB (extended in dotted line), 
the characteristic pressure-distance curve for the conical nozzle. Note 
how very rapidly the pressure falls just beyond but near to the throat, 
or how little enlargement of section is needed to accommodate a big 
range of pressure drop in that region. 

The same diagram is further intended to illustrate what happens 
when the nozzle expands too much, or has too great an area ratio for 






§ 47 (/)] 



EXPERIMENTS ON THE STEAM JET. 



461 



the existing pressure ratio. In the figure, with R p equal to 0.3, drop 
to this P2 is accomplished at CD, and the nozzle should end there. In 
the extension of the nozzle, orderly jet formation continues to some 
lower pressure — we may say, of its own inertia : then a sudden change 
of condition and action occurs, and the pressure begins to rise. This 




Fig. 332. — Curves of Pressure Variation in a Long Nozzle: experiments by Stodola 
diagram redrawn from Stodola's Steam Turbines. 

involves a considerable dissipation of progressive velocity into secondary 
motions, and the reconversion of kinetic energy into pressure work as 
the stream is retarded and compressed. By the time the jet gets to 
the mouth of the nozzle, it has far less available energy than at B, and 
a correspondingly larger heat content. 



462 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 

The induction of a local pressure much less than the final pi accounts 
for the early establishment of full flow in the divergent nozzle of Fig. 328. 
In effect, the nozzle exerts a sort of suction; and when pi is greater than 
p this induces at the minimum section a pressure lower than p 2 , hence 
gives increased flow. But as soon as the zone of least pressure passes 
beyond (to the right of) the throat, the flow becomes practically fixed 
in rate. 

Figure 332 serves as a very good representative example of results 
got by means of the search tube, covering a wide variation of final 
pressure with a nearly constant initial pressure. This diagram shows 
the realized form of the action which is merely sketched in Fig. 331. 
The rise of pressure just beyond the minimum is almost an abrupt jump, 
indicating something like a shock in the change of flow condition. At 
the lower discharge pressures, curves G to K, appear the wave lines of 
incipient acoustic vibration. The sound wave, having a fore-and-aft 
oscillation in the direction of its propagation, sets up in the steam current 
alternating zones of higher and lower pressure. 

Stodola, to whom the reader is referred for further information, 
gives a number of sets of curves of this type. Many of them come from 
what obviously are not proper forms for steam-turbine nozzles, and, 
by the exceeding badness of the action which they show, fulfill the in- 
tention of confirming the conclusions of reason and common sense as 
to what are likely to be proper forms. Of greatest interest after Fig. 332 
is a group of curves from a convergent nozzle, or " orifice" with rounded 
entrance: the investigation is carried well beyond the plane of outlet, 
and shows a very rapid drop of pressure when p 2 is less than p . Well- 
marked vibrations appear, of moderate magnitude when p 2 is about 
equal to p , increasing as p 2 falls, then diminishing as p 2 becomes very 
small. 

(g) Tempekature Gradient in the Jet. — Complementary to the 
idea of localized pressure measurement, that of similar temperature 
measurement has been applied in a few experiments. Sample results 
are given in Fig. 333, which shows observations made by both methods, 
in the De Laval nozzle at the top of the figure: steam of 60 lb. initial 
gage pressure was discharged into the atmosphere, this initial pressure 
being so low that there was overexpansion in the nozzle. The curves 
or point series, taken in order as lettered, are as follows: 

Curve A, to scale at left, is pressure measured by means of a search 
tube which ran clear through the nozzle and had a hole drilled squarely 
across it, in the usual fashion. 

Curve B is pressure measured by a search tube open at the end and 
projecting into the nozzle from the entrance side, so that the opening 



§ 47 (g)] 



EXPERIMENTS ON THE STEAM JET. 



463 



was in the direction of flow. It is evident that the abrupt enlargement 
of cross area at the squared-off end of the tube must have had a very 
considerable effect upon the local pressure gradient, and that the differ- 
ence between B and A is by no means all due to suction of the eddy at 
the end of the tube. In fact, beyond the beginning of the sloping nozzle 
mouth, where area ceases to be determinate, the two pressures become 
scarcely distinguishable. 

Curve C shows measurement of pressure by an open-end tube thrust 



80 
10 
60 

50 
P 
40 
Lb. 

30 
Abs. 

20 

10 



T 

(£> 
O* 



•D^ 



"*&€** 



.25" 



^-044Me-Q66' H 



0.17" 



••D 



A + 



^£ 



^ 



t* 



*r 



+ ^ ++ . 



0.241 



r-W ■ » • » 



^ 



H 



i* 



±t±++ 



+?r 



c 

PO QQ-OO-Q-g- 

B 



o C 



4^+t*# 



+:r:*******m 



* +* +^+ 



340 

320 

300 

280 

260 
t 

240 
Dec. 
220 

Fahr. 

200 

180 



0.5 



Inches 



1.0 



1.5 



2.0 



2.5 



Fig. 333. — Results of Pressure and Temperature Measurements, tests by Borsody 
and Cairncross at Columbia University. Reported by Prof. C. E. Lucke, 
Trans. A. S. M. E., 1905, Vol. 26, 114-158. 

into the nozzle from the discharge side. Here again, abrupt change of 
section must produce some disturbance of flow; but it appears that a 
large part of the velocity "head" is converted into static pressure in 
the measuring tube, even when the density of the steam in the jet has 
become quite low. 

Curve D, to scale at right, gives the temperature in the steam, as 
measured by a thermocouple, of which the joined wire was stretched 
along the axis of the nozzle and moved lengthwise just like the pressure 
tube. 



464 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Curve E is the temperature of saturated steam corresponding with 
measured pressure A, laid out in order that D may be compared with 
it. The steam was superheated at the start. In very peculiar fashion, 
temperature D at first falls below E; but it soon reverses relation and 
runs from 30 to 20 deg. above E. Rationally, after nearly adiabatic 
expansion has (very soon) brought the steam out of the region of super- 
heat into that of saturation, the temperatures ought to coincide. If 
curves D and E were fairly near to each other, and a close comparison 




Fig. 334. — Reaction upon the Nozzle, tests by W. Rosenhain, at Cambridge 
University. Proc. Inst. C. E., 1900, Vol. 140, 199-220. 



worth while, difference in effective variant area ratio and in pressure 
gradient, due to the substitution of small wire for larger tube, would 
have to be taken into account in bringing them to a common basis. 
With actual data, the comparison has nothing but the roughest qualita- 
tive value. 

In connection with the preceding may be cited some experiments 
by C. Batho, at the University of Liverpool, reported in Proc. Inst. 



§ 47 (g)] EXPERIMENTS ON THE STEAM JET. 465 

C. E., 1907-08, Vol. 174, 317-331. A thermocouple was used in essen- 
tially the same way. With a brass steam nozzle, the observed tempera- 
ture ran a little below that from the calculated pressure gradient until 
near the end of expansion, then rose above it. With a porcelain nozzle, 
lined with glass which was carefully ground to form and polished, the 
measured temperature kept about 20 deg. above the theoretical. Some 
rather unwarranted conclusions were drawn as to relative losses of heat 
or transfer along the nozzle. 

The matter seems to be best summed up by the statement that the 
temperature method has shown itself distinctly unreliable in this par- 
ticular line of work. 

(h) Efficiency in Jet Formation. — This is measured by the ratio 
of actual kinetic energy of the jet, as delivered by the nozzle, to calcu- 
lated available energy of the steam according to the Rankine cycle. 
Actual energy becomes known if we can find the velocity of the steam : 
and while velocity itself would be exceedingly difficult to measure, the 
simple relation of velocity to impulse or reaction leads at once to the 
idea of measuring that force. 

Experiments have been made in which a flat plate was held in front 
of a nozzle, at a short distance from the mouth,* as indicated in Fig. 303. 
These give a fairly good determination of impulse, but it is difficult to 
eliminate secondary disturbances which interfere with accuracy. The 
scheme outlined in Fig. 304 is inherently rather better, but must be 
used with due regard to the considerations set forth in § 46 (6) and 
Examples 42 and 43. We shall first review some earlier experiments in 
which the relations involved were not fully taken into account. These 
will lead up to some thoroughly correct tests, which give very good 
illustration of the reaction method, and also of the indirect method of 
calculating efficiency from observed pressure in the jet. 

(i) Rosenhain's Reaction Tests. — In Fig. 334, the principal 
series of plotted points shows measured reactions, due to discharge into 
the atmosphere of steam of varying initial pressure, through the rounded 
orifice A and the full nozzle B as outlined at the top of the diagram. 
The points along the lines marked W give rates of flow in pounds per 
second, two lines of calculated flow being necessary because of slightly 
different minimum diameters in the two cases. For comparison with 
the reaction points, a number of theoretical curves or lines are drawn, 
as follows: 

Line CD shows the dynamic reaction Fa resulting from expansion 
to p = 0.58 pi in orifice A, calculated after the manner of Example 42, 

* For example, by E. Lewicki at Dresden, published in Zeitschrift des Vereines 
deulscher Ingenieure, 1903, page 491. 



466 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



using the ideal discharge in Eq. (237). Based on Tables 6 and 7, which 
assume similarity of jets from different initial pressures, when referred 
to the pressure ratio R p , CD is a straight line. 

Line ED adds to Fa the static-pressure reaction (p — p 2 ) X a , 
giving the total calculated reaction R&. At D, where pi = 14.7 -5- 0.58 
= 25.4 lb. abs., the orifice pressure p is just equal to the external pres- 
sure, and the reaction measured is purely dynamic. Above D, or for 
practically the whole range of this particular experiment, the observed 
reaction is of no value at all as a criterion of jet formation. 




Fig. 335. — Observed and Corrected Reactions, Sibley and Kemble Tests, 
reference under Fig. 329. These data belong to nozzle 14 in Fig. 330. 



See 



With the expanding nozzle B, lines FG and KG give Fb and Rb in 
the same manner. These lines meet at a comparatively high pressure, 
since the nozzle has an area ratio a 2 /a = 2.435, for which R p = 0.098 
by Table 6: wherefore the initial pressure which will just reduce to that 
of the atmosphere is pi = 14.7 -s- 0.098 = 150 lb. abs. With pi less 
than 150, there is overexpansion in the nozzle. If, as is probable, the 
variant pressure p rises to p 2 within the nozzle, as indicated in Fig. 331, 
comparison of measured Rb with the ordinate of line GH will show 
the proportional loss of velocity caused by excessive divergence. 

Only at or near G, where a short curve is traced through several 
experimental Rb points, can the efficiency of the nozzle properly be 
derived from these experiments. At G, the measured reaction is only 



§ 47 (i)] EXPERIMENTS ON THE STEAM JET. 467 

1.6 per cent below the ideal; but as appears from the W comparison, the 
former is produced by about 1.05 times as much steam as the latter. 
Dividing 0.984 by 1.05, we have 0.933 as the ratio of reactions, or of 
actual to ideal velocity. Squaring this ratio, because kinetic energy 
varies as square of velocity, we get an efficiency ratio of 0.87. 

It is evident that any comparison among different nozzles in this 
group of tests, based simply on observed reactions, without any analysis 
such as has just been exemplified, must be inconclusive and of little 
value. 

(j) The Sibley and Kemble Tests. — These experiments, already 
introduced in Art. (d) , combine the reaction and the search-tube method 
in a manner which is really necessary if definite results are to be obtained 
by the former. The arrangement was essentially that of Fig. 304, and 
similar to Rosenhain's except that both the nozzle chamber and the 
flexible steel tube carrying it were enclosed in a box which was connected 
to a condenser. The dynamometer was a pulling spring, and with any 
load this was adjusted so as to bring the reaction chamber to its neutral 
position, thus eliminating any elastic resistance of the tube to bending: 
the extension of the spring, or the displacement of the screw slide carrying 
its front end, measured the reaction. For search-tube work, the nozzle 
box was clamped, and the tube coupled to a gage connection. Only 
the pressure in the mouth of the nozzle, at or just within the terminal 
cross plane, was sought: and beside the search tube in nozzles 9 and 13, 
Fig. 330, every nozzle had a small test hole drilled in its -wall just inside 
the end plane. 

The purpose in measuring the mouth or muzzle pressure in the 
nozzle will be made clear by a study of Fig. 335, which shows a typical 
set of reaction observations, one group for each of the four initial pres- 
sures already named in Fig. 329. The base is absolute pressure pb in 
the vacuum box surrounding the nozzle chamber, called the " box 
pressure." With a fixed initial pressure, as pi = 145 lb., and with a 
resulting constant terminal pressure p 2 due to expansion within the 
nozzle to the final cross area a 2 , the measured reaction varies as shown 
by the points along the inclined line AB: it is greater with a low box 
pressure, less as pb increases — this being in accord with the statements 
in § 46 (6), under Fig. 304. Subtracting or adding the force got as the 
product of pressure difference (p 2 — Pb) by area a 2 , the points along 
the horizontal line CD are found. The height of this line is the true 
dynamic reaction, as the mean of a number of determinations; and the 
intersection E shows, on the base scale, the terminal pressure p 2 in the 
nozzle. A simple locus EF, within the limits of these experiments a 
Straight line, connects the several values of p 2 . 



468 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Table 19. Efficiency Results, Nozzle Tests by Sibley and 
Kemble. Nozzles Nos. 11 and 14 in Fig. 330. 



Quantity. 


Nozzle 14. 


Nozzle 11. 


Pi 


145 


130 


115 


100 


145 


130 


115 


100 


Vi 


1.632 


1.460 


1.288 


1.116 


0.929 


0.832 


0.735 


0.638 


F 


17.82 


15.98 


14.15 


12.30 


18.13 


16.24 


14.35 


12.45 


W 


0.1550 


0.1394 


0.1239 


0.1081 


0.1536 


0.1383 


0.1228 


0.1069 


v r 


3698 


3685 


3672 


3659 


3796 


3776 


3759 


3744 


E T 


273.2 


271.3 


269.5 


267.5 


288.0 


285.0 


282.4 


280.1 


E t 


290.9 


289.5 


287.8 


286.1 


318.6 


317.1 


315.3 


313.2 


e T 


0.939 


0.938 


0.937 


0.935 


0.904 


.0.899 


0.895 


0.895 


a 2 


6.45 


7.16 


8.06 


9.24 


10.37 


11.52 


12.98 


14.92 


I 1.00 


6.32 


7.05 


7.96 


9.16 


10.04 


11.18 


12.65 


14.54 


a t }0.95 


6.59 


7.36 


8.32 


9.56 


10.51 


11.70 


13.23 


15.21 


(0.90 


6.90 


7.69 


8.72 


10.00 


11.00 


12.26 


13.85 


15.93 


e a 


0.976 


0.982 


0.986 


0.990 


0.965 


0.967 


0.972 


0.975 



Experiments by F. H. Sibley and T. S. Kemble, at Case School of Applied Science, Cleveland, Ohio. 
Trans. A. S. M.E., 1909, Vol. 31, 617-653. All quantities below E r recomputed or newly computed by the 
writer, with values from the steam tables in this book. 

(k) Calculation of Efficiency. — Having initial pressure and 
quality of steam, rate of flow, reaction on the nozzle, and terminal 
pressure within the nozzle, efficiency in the generation of kinetic energy 
may be calculated in two ways, both of which are illustrated in Table 19. 
The description of this table may well be accompanied by an outline 
of the principal calculations, with numerical values from and for the 
first column. The various quantities and their derivation are as 
follows : 

Pi initial steam pressure, pounds per square inch absolute. At pi 

the steam is taken to be dry-saturated: in some tests it showed 

a trace of superheat, in others there may have been a little 

moisture present. 
P2 is the terminal nozzle pressure, determined as in Fig. 335. Note 

the lower values prevailing with the larger area ratio of nozzle 11. 
F corrected dynamic reaction, also determined by the construction 

in Fig. 335. 
W rate of flow or discharge, in pounds per second. On Fig. 229, 

short vertical lines in the test groups for nozzles 11 and 14 show 

the flow values used by the experimenters. 
V T velocity by reaction, from Eq. (214); 

T/ Fg 17.82 X 32 .16 

V — ttt = r> 1gc ^ — = 3698 ft. per sec. 

W 0.1550 



§ 47 (k)] EXPERIMENTS ON THE STEAM JET. 469 

E T kinetic energy of the j et per pound of steam, reduced to heat units ; 

F 2 _ 13,675,200 
^ " 2 g X 778 ~ 64.32 X 778 " Z76Z ti ' t ' }1 ' 

E t available energy per pound of steam, within the limits p\ and p 2 , 

by the methods of § 15 (d) : detailed calculation in Example 49, 
following. 

e T efficiency as found by the reaction method; 

h. = ?Z^ = o 939 
6l E t 290.9 U ' ydy * 

a2 terminal area of a unit jet similar to that actually observed. 

The muzzle area of nozzle 14 being 0.9993 sq. in. (Fig. 330) and 
the rate of flow 0.1550 lb. per sec, the unit area is 

0.9993 aAS 
a2 = Ol550 = 6 - 45sq ' m - 

a t calculated area a 2 , with various efficiencies. Value marked 1.00 

is for the ideal jet with adiabatic expansion; those marked 0.95 
and 0.90 are for these efficiencies. That is, we assume that 
5 or 10 per cent of the available energy Et is retained in or 
returned to the steam as heat. This makes velocity V less 
and specific volume v greater, hence increases a when calculated 
by Eq. (105): see Example 50, on page 471. 

e & efficiency by the search-tube method. Interpolating a 2 between 

the 0.95 and the 1.00 values of a t , we have that 6.45 is 14/27 
of the way from 6.59 to 6.32, so that the efficiency must be 
0.52 of the way from 0.95 to 1.00, or at 0.976. 

Example 49. — The calculation of the ideally available energy E t for the 
first column of Table 19 is as follows: 

Initial pressure pi = 145 lb. abs. 

Initial quality X\ = 1.00 

Final pressure p 2 = 1.632 lb. abs. 

Final temperature, Table II, t 2 = 118.78 deg. 

Final total entropy at P 2 , N 2 = 1.93482 

Initial entropy, at p h Ni = ?ii = 1.57248 

The value of ri\ remaining constant during adiabatic 
expansion, the steam at p 2 has from full vapori- 
zation the shortage N 2 — n x = 0.36234 

At p 2 , the entropy of vaporization is b 2 = . . . , 1.7725 

Then the fraction of condensation is 

m 2 = (Nt-ni) -62 = 0.20443 

Latent heat at p 2 , r 2 = 1025.2 B.t.u. 



470 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 

Total heat at p 2 , H 2 = 1111.81 B.t.u. 

Heat deficiency, m 2 r 2 = 209.57 " 

Actual heat content at p 2 and m 2 , h 2 = .... 902.24 " 

Initial total heat Hi or hi = 1193.17 " 

Available energy E = hi - h 2 = ....... 290.93 " 

(I) Efficiency by Condition of Jet. — The scheme of the second 
derivation of efficiency in Table 19, leading to e a , is illustrated in Fig. 336. 
For various ratios of realized kinetic energy to quantity of heat ideally 
convertible, are worked out and plotted, first, the area a of the unit or 



0.20 




Fig. 336. — Calculated Terminal Proportions of the Steam Jet. Initial pressure 
uniform at 145 lb. per sq. in. absolute, initial quality 1.00, terminal pressure 
variable. 



pound-per-second jet in square inches; second, the rate of flow W/a 
in pounds per square inch per second. Line PP is drawn at the ter- 
minal pressure p 2 = 1.632 of column 1 in Table 19. Efficiency e a can 
be found either by interpolating point A between the a-curves for 1.00 
and 0.95, as above, or by interpolating W/a at B. In order to make 
this determination, the rate of flow and the pressure in the steam at an 
accurately located section of the nozzle must be known. With more 
emphasis placed upon a certain area than upon a local pressure, point 
A would be interpolated on a horizontal line, for the observed pi) but 
what is here vertical interpolation has the advantage that the area 
corresponding to a given pressure and efficiency can be calculated, while 
the theoretical pressure at a given area cannot, but must be found 
indirectly, from a graphical layout of results by the other method. 

In the procedure just outlined, nothing is said about " ideal" dis- 
charge, as calculated from the throat area, so that relations are simpler 



§ 47 (I)] 



EXPERIMENTS ON THE STEAM JET. 



471 



than in Fig. 334. For the ideal case of unit efficiency, identity with 
that rate exists; but in all other cases it is better, as here, to confine 
attention to the particular cross section under consideration. 

Example 50. — Find the three at values in the first column of Table 19, 
using quantities from the last example as convenient. 

The full ideal energy is E t = 290.9 B.t.u. 

One-tenth of this is AE = 29.1 " 

With r 2 = 1025.2, addition of 29.1 B.t.u. to the heat 
content will change the moisture fraction by the 
amount Am =29.1 -r- 1025.2 = 0.0284 

Then for the three cases of 1.00, 0.95, and 0.90 effi- 
ciency, m will have the respective values 0.2044, 0.1760, 0.1476 

The velocity with-# = 290.9 is by Eq. (104), 

Fi.oo = 223.7 V290.9 = 3815.7 ft. per sec. 

For the other cases, instead of repeating this calcula- 
tion, it is easier to look up the square roots of 
0.95 and 0.90, getting 0.9747 and 0.9487;* then 
subtract from Vi. 00 the fractions 0.0253 and 
0.0513 of itself, with the results, 

Fo. 9 5 = 3719.2, F . 90 = .... 

The full specific volume at p 2 is s 2 = . . . . 

For the 1.00 case, ra 2 s 2 = 210.3 X 0.2044 = . . 

Also, for 10 per cent change, Am X s 2 = . . . 



Then the respec-^j 
tive volumes > 
are J 

Now by Eq. (105), 



^1.00 

4 ^0.95 

^0.90 



= 210.3 - 43.0 
= 167.3 + 3.0 
= 167.3 + 6.0 



3620.0 ft. per sec. 
210i~eu. ft. 
43.0 



144 v 144 X 167.3 
a - — , fll .oo 3^ 



5.96 
167.3 
170.3 
173.3 



6.32 sq. in., 



and the other areas are found in the same way. 

(m) Results as to Efficiency. — Considering first the results in 
Table 19, we note in e T a prevailing difference of nearly 4 per cent be- 
tween nozzles 14 and 11. With the longer expansion in No. 11, there 
must be a little more energy lost; but it does not seem reasonable that 
the ratio of this loss to the available energy (itself a rapidly increasing 
quantity) should increase in any marked degree. To use equal flow 
rates, instead of one per cent less for No. 11 as appears in Fig. 329, 
would bring the efficiencies nearer together — remembering that a 
small proportion of change in velocity V is doubled when squaring V to 
get energy E. 

* The idea being to use the slide rule for as much as possible of the numerical 
work. 



472 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 

Why the efficiency e a by area should be so much larger than e T by 
reaction is not apparent; but it seems that more credence ought to be 
given to the results by measurement of dynamic force than to those 
found by a very indirect derivation. The experiments set forth in 
Table 19 are, so far as the writer knows, the best that have been made 
(and published) to determine the efficiency of the operation of forming 
a steam jet in the divergent nozzle. They illustrate fully the need 
of great accuracy in the measurement of the principal quantities; and 
the marked difference between results by the two methods, or between 
e T and e a > indicates most decidedly that there is much yet to be learned 
about the intimate detail of the behavior of the steam in the jet. The 
problem is, however, one for the physicist rather than the engineer. 

As regards the various nozzles shown in Fig. 330, reactions were 
measured with Nos. 10, 12, and 15, beside 11 and 14. No difference 
seems to have resulted from the wide angle of No. 12 or the change of 
shape in No. 15. 

In Art. (i), from experiments perhaps not very exact in rate of flow, 
we deduced an efficiency of 0.87 for a De Laval nozzle discharging into 
the atmosphere. Stodola, in Fig. 27 of second edition of Steam Turbines, 
shows results by the method of Art. (I) from a nozzle about 0.5 in. in 
throat diameter and discharging 0.34 lb. of steam per sec. from 149 lb. 
abs. into a good vacuum : the plotted points agree very closely with the 
curve for 10 per cent loss of energy. Continuing, he quotes determi- 
nations of Delaporte and of Lewicki by the impulse method suggested 
in Fig. 303, which gave efficiencies of 0.95 and 0.93, with flow from 
De Laval nozzles into the atmosphere. 

Briling,* using this same impulse measurement with cylindrical and 
with slightly convergent nozzles, and discharging into atmosphere 
from initial pressures so low that the ratio R p = P2/P1 does riot fall 
below 0.58, gets a ratio of from 0.92 to 0.97 for actual to ideal velocity, 
or an efficiency of 0.85 to 0.94 — this increasing with higher velocity or 
greater pressure range. 

Experimental knowledge on this subject may be summed up in the 
statement that the probable efficiency of properly proportioned nozzles 
is from 0.88 to 0.93. By proportion is meant especially the ratio of 
divergence or the area ratio a 2 /a . In general, it is decidedly more 
harmful to have this too large, causing overexpansion, than to have it 
too small. As appears from Fig. 336, if the area a 2 be designed for the 
ideal case it will be a little small for actual conditions; wherefore the 
ideal proportions may properly be used with little or no modification. 

* Zeit. Ver. deutsch. Ing., 1910, Vol. 54 I, 265, etc. Verluste in den Schaufeln 
von Freistrahldampfturbinen, 



§ 47 (n)] EXPERIMENTS ON THE STEAM JET. 473 

(n) Flow in Curved Channels. — As may be inferred from the 
calculation of centrifugal pressure in Example 44, page 438, a current 
of steam flowing in a curved channel is subject to forces which certainly 
do not tend to maintain orderly flow in " parallel" stream lines, on the 
hypothesis represented in Fig. 305. With any considerable width of 
channel relative to radius of curvature, such as always exists, there must 
at the very least be a crowding of the stream against the outer wall, 
after the mftnner depicted at I in Fig. 337. But it is evident that this 
sketch gives a very inadequate idea of what takes place: rather, with a 
stream entering tangentially as at II in Fig. 337, the curved guide sur- 
face may be regarded as cutting obliquely (and quite sharply) across 
the line of flow; then this surface will not only deflect the current (or 
give it transverse acceleration) but will also produce some linear retar- 
dation. Instead of sweeping smoothly around the curve, the jet will 
pile into the bucket in a confused and tumultuous fashion, with a rise 
of average pressure throughout the confined space; and from this broken 
and compressed stream the escaping jet will again be formed, with 
pressure drop, in a manner much like that which of intention prevails 
in the reaction turbine. 

Observations of Pressure. — Stodola (Fourth Edition, Berlin, 1910, 
pages 95 to 102) gives the results of experiments made to find the vari- 
ant pressure within curved nozzles and blade channels. These were of 
rectangular cross section, and one plane wall was a movable plate, with 
a search hole which could be brought to any desired position. The 
curved nozzles were of the general form of those in Fig. 19, or much 
like the ordinary reaction-turbine blade channel: there was some " bank- 
ing up" of the current against the concave side, but comparatively 
little, because by the time high velocity was attained the channel had 
become nearly straight. With a row of impulse vanes held in front of 
the nozzle, and with observations represented by curves of equal pres- 
sure very similar to the curves of equal altitude on a topographical map, 
some interesting results are shown, in Stodola's Fig. 88. The nominal 
expansion was from 155 lb. absolute to atmospheric pressure; but the 
standing vanes backed the pressure up to about 28 lb. in the mouth of 
the nozzle. At the middle cross section of the blade channel which, 
being squarely in front of the nozzle, received full inflow — the plane 
of this section being perpendicular to the channel walls and to what 
would be the axis of wheel rotation — the pressure varied from about 
105 lb. against the outer guide surface, or in the bottom of the bucket, 
to about 40 lb. near the inner surface; and at the outlet of the channel 
it was still about 20 lb. abs. 

Increase of Radial Depth. — Of course, this action involves a loss of 



474 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



progressive kinetic energy and of stream velocity. Its most striking 
practical effect is seen in the prevailing departure of construction from 
the conclusions stated at the end of § 46 (k) . With no secondary 
losses, no increase in the radial length of the vane, or in the depth of 
channel, would be called for; but because of large bucket loss such as 
has just been indicated, experience has shown the need of a decided 
increase of radial depth, to provide a sufficient enlargement of flow 
area — see the sections of Curtis wheels in Figs. 23 and 359. Without 
such gradual enlargement, the current would back up and the pressure 
be higher on the nozzle side of the wheel. These remarks refer espe- 
cially to multiple-impulse wheels of the Curtis type, but apply in a lower 
degree to single vane rows in the stage. 

Non-symmetrical Vanes. — If a vane channel is curved clear to 
exit, as in Fig. 337 II, the stream will have some tendency to curl over 
the outer edge, swinging away from the tangential direction there 






Fig. 337. — Behavior of the Jet in the Bucket or Vane Channel. 

represented by dotted lines. To compensate for this and get a larger 
driving component from the reaction of the escaping jet, impulse vanes 
are now often made as shown at III in Fig. 337, with a narrower angle 
of exit ABD than of entrance AFC. 

Limitation of Velocity Staging. — The obvious impossibility of mak- 
ing a steam current of intended uniform pressure follow a tortuous 
path in orderly flow accounts for the limitation which experience has 
placed upon velocity staging, or upon what in this book is called mul- 
tiple-impulse action. Thus in the service of driving electric generators, 
large Curtis turbines are now never made with more than two vane 
rows to the wheel, as against three in a few early examples. The use 
of three or in some cases four rows on a wheel, under the lower-speed 
requirements of marine service, must involve loss of efficiency. The 
Riedler-Stumpf type of arrangement, with tangential buckets and with 
long curved return channels, as shown in Fig. 354, has been definitely 
given up for large and efficient turbines. 



§ 47 in)] EXPERIMENTS ON THE STEAM JET. 475 

In this connection, it is of interest to refer to some results given by 
Stodola (Fourth Edition, page 100) of pressure measurements along the 
guide channels of a small Elektra turbine. The machine was generally 
similar to that in Fig. 352, but had only one pressure stage, with four im- 
pulses. At the four places where the steam current, after leaving the 
nozzle, flowed between and acted upon the moving vanes, it had the pres- 
sures 4.7, 6.4, 2.8, and 1.5 lb. abs., a considerable rise occurring in the first 
guide channel. A descending pressure gradient beyond the nozzle is, 
of itself, an influence toward better performance; and this particular 
turbine is better adapted than are most small multiple-impulse designs 
to the task of holding in a definite channel a current of. varying pressure, 
without much leakage or spilling. 

(o) Impulse upon Vanes. — A good many experiments have been 
made in which a group of turbine buckets was held in front of the nozzle 
in working position, being supported by a weighing device capable of 
measuring the force exerted upon the vanes by the steam jet. From 
this force, with due regard to the angles of entrance and of exit, may 
be calculated the apparently realized mean velocity of the jet; but the 
method is hardly good for more than rough approximations, and the 
results must be used with care. 

In Thomas' Steam Turbines diagrams are given showing a large 
number of observations of this kind: but they are much diminished in 
value by, the fact that the nozzles used were not adapted to the con- 
ditions of working. With atmospheric pressure as p 2 and with pi vary- 
ing from 30 to 110 lb. abs., the nozzles were all cylindrical but one, and 
that had a degree of divergence so large that it would be necessary to 
raise pi to more than 400 lb. in order to avoid overexpansion in the 
nozzle. The ratio of actual velocity (calculated from observed impulse) 
to ideal velocity ranges from 0.65 to 0.80, which corresponds with an 
energy efficiency of 0.40 to 0.64. If the nozzles had been proportioned 
to the pressure ratio, these results might have been considerably im- 
proved upon. 

Stodola (Figs. 47 to 50 of the Second Edition) gives some curves 
showing the reactions observed with a similar arrangement; but in 
failing to supply quantitative data as to size of nozzle, rate of flow, etc., 
makes evident that he considers them merely of illustrative value. 

(p) Impulse of Jet Leaving Vanes. — In the experiments of Bril- 
ing the arrangement was as outlined at I in Fig. 338. A group of vanes 
was held fixed in front of the nozzle, and the flat measuring plate was 
set squarely across the current leaving the vane channels. This gave 
an impulse which was compared with that got by setting the plate in 
front of the nozzle itself, the ratio serving as a velocity coefficient, 



476 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



which in terms of the velocity diagrams in § 46 has the value 

e v = V 2 + V 1 



(239) 



The angles and spacing shown in Fig. 338, and found by test to give 
the best results, agree well with general practice. With these propor- 
tions, the coefficient E y ranged from 0.50 to 0.75, rising by 0.10 to 0.12 
with change from the smallest to the largest vanes tried. At II the 
dotted outline added to the first vane shows the profile that would be 




Fig. 338. — Smallest and Largest Blades used in Briling's Experiments — see 
reference on page 472: intermediate sizes had widths of 15 and 20 mm. 

needed to give a channel of uniform width; while the actual vanes were 
made of brass plate, bent to curve and ground off at the edges. Varying 
the spacing or pitch, it was found that e v grew less with change in either 
direction from the setting in Fig. 338, where pitch equals radius of 
curvature. Greater loss with closer spacing was attributed to more 
friction on the relatively larger amount of guiding surface; but it looks 
as if relatively greater width of the pocket between the vanes would be 
an even stronger influence toward wasteful action. With wider pitch 
there was, naturally, a poorer control and less definite deflection of the 
current. 

Other vane profiles were tried, with entrance and exit angles of 20, 
40, and 50 degrees, beside the 30° angles in Fig. 338: the swing or de- 
flection of the current is less as the edges are more inclined, being 140° 
with 20° edge angles, only 80° with 50° edges. The smaller the angle 
of deflection, the less was the loss of velocity, ratio e v going above 0.80 
with 50° vanes. Over the range of experiment, with steam velocities 
of 250 to 1400 ft. per sec, the coefficient e v increases slightly with rising 
steam velocity. 

From data in the first part of Table 20, it may be estimated that the 
best running efficiency of the turbine wheel represented by the con- 
ditions of these experiments might be about 0.45 — this being, for the 
combination of nozzle, vanes, and wheel, the ratio of useful output to 



§ 47 (p)] EXPERIMENTS ON THE STEAM JET. 477 

energy ideally available. The square root of 0.45 is 0.67, and is com- 
parable with E v ; whence we see that Briling's results check up fairly 
well as to order of magnitude; still, their value is qualitative rather than 
quantitative. 

(q) Energy Losses in the Turbine. — The total deficiency from 
ideal output is made up of losses in jet formation and in jet application, 
of residual kinetic energy in the jet when it leaves the vanes, and of 
friction work. The first item, jet formation, is most open to investi- 
gation, as may be inferred from the amount of space that has just been 
given to nozzle action. Loss in jet application, through steam friction, 
steam shock, stray motion, and leakage, is decidedly the largest item; 
but the possibility of following it out in detail in the running machine 
is very slight. Loss by residual energy is generally made quite small, 
and can be fairly well estimated or inferred. Friction includes both 
resistance to spinning of the rotor in the steam atmosphere which sur- 
rounds it and machine resistance in the bearings: its work absorption 
may be found by motor-driving the turbine or, in some cases, by shut- 
ting off steam and observing how rapidly the rotor loses speed because 
of friction, all external load having been taken off. 

From the preceding statement it appears that in an analysis of 
turbine action the larger part of the energy loss must be determined 
by subtracting several smaller parts from the total loss. The latter 
is easily found, being one of the principal results from any performance 
test. Whether from the view-point of detailed analysis then, or with 
the simpler and more useful purpose of showing what the turbine can 
do, the presentation of test results is now in order. 

§ 48. Turbine Performance 

» 
(a) Scheme of Table 20. — This collection of turbine data is 

generally similar to that for the engine in Table 13, pages 268 to 271, 

although some changes in the form of the quantities have been made. 

To save the trouble of referring back, all the symbols will now be briefly 

defined, with fuller explanation of points peculiar to the turbine. 

Pages A, D. Description, Authority, Reference, etc. 

First two groups (small turbines) and last group (low-pressure tur- 
bines) are determined by a controlling condition of operation. Between 
these the arrangement is by type: single-impulse wheels (Rateau, 
Zoelly, etc.); several-impulse wheels (Curtis, Schulz); combination of 
these two types (A.E.G. = Allgemeine Elektrizitats Gesellschaft) ; 
reaction turbines (Parsons and variations); combined impulse and 
reaction types. 



478 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX 

Table 20, page A. Tests of Various Steam Turbines. 



No. 



Size, Make, Authority, Reference, etc. 



6 

7 

8 
9 

10 
11 
12 

13 
14 
15 
16 



17 



18 
19 
20 

21 

* 

22 
23 
24 
25 

26 

27 



28 



Small Noncondensing Turbines. 

30 h.p. De Laval, E. Lewicki, Dresden, 1901; Z.V.D.I., 1903, Vol. 471, 
494. 

! 25 h'n Terrv TW 293 1 Pa P er > " Sma11 Steam Turbines," G. A. 

in £' P " n J' p Hi > Orrok, Trans. A.S.M.E., 1909, Vol. 31, 
50 h.p. Curtis, rage 285 f 9A o om 

200 h.p. Curtis, Page 285 J ^ 6 6L{J ' 

Small Condensing Turbines. 

30 h.p. De Laval, E. S. Lea, Trans. A.S.M.E., 1904, Vol. 25, 1069. 

50 h.p. De Laval, T. B. Morley, Glasgow, 1905; Engineering, 1905 II, 

Vol. 80, 880. 
100 h.p. De Laval, Lodz, 1901; Z.V.D.I., 1901, Vol. 45 II, 1678. 
300 h.p. De Laval, Dean & Main, Trenton, 1902; Engineering Record, 

1902 II, 100. 
20 h.p. Elektra, A. Stodola, 1906; i H. Meuth, Z.V.D.I., 1908, Vol. 
200 kw. Elektra, Builders; > 52 I, 182, 216; also Stodola IV, 

200 kw. Elektra, Prof. Hubert; ) 374. 

0/1 , -n AT i.i . '■ ' 1 Paper, " Trials of Steam Turbines 

24 kw. Parsons, Newcastle, £ .^ Dynam0Sj » C . A. Parsons 

50 kw. Parsons, Blackpool, ^ and Q *» G / Stone ^ Int . E Con _ 

200&:pSS;S^1; [ ^W;*^^,^!!^^ 

Large One-stage Turbine. 

1400 kw. Riedler-Stumpf, Moabit Station, Berlin, 1902, 3; F. Rotscher, 
Z.V.D.I., 1907, Vol. 511, 605, etc.; see Stodola also. 

Single-impulse Turbines. 

500 h.p. Rateau, A. Stodola, Paris, 1903; Stodola HE, 267; IV, 428. 
1000 kw. Rateau, Oerlikon Works, 1903; Stodola II E, 261. 
1000 kw. Rateau, Oerlikon Works, recent; Stodola IV, 435. 

1500 kw. De Laval, Varberg, Sweden; Power, May 3, 1910. 

300 kw. Zoelly, 3000 r.p.m. ^ 

700 kw. Zoelly, 3000 r.p.m. 1 Z.V.D.I., 1910, Vol. 54 1, 330; Stodola IV, 
1000 kw. Zoelly, 3000 r.p.m. [ 421, Table 4. 

2300 kw. Zoelly, 1500 r.p.m. J 

5000 kw. Zoelly, 1000 r.p.m., Reinisch-Westfalischen Elektricitatswerk, 
1908; Engineering, 1908 II, Vol. 86, 1; Stodola IV, 420. 

3500 kw. Zoelly, 1500 r.p.m., Alsace Mach. Co., Mulhouse; Z.V.D.I., 1910, 
Vol. 54 II, 1500. 

Several-impulse Turbines. 

500 kw. Curtis, 1800 r.p.m., G. H. Barrus, Newport, 1904; Bulletin. 



A.S.M.E., American Society of Mechanical Engineers. Up to Vol. 31, 1909, references are to the com- 
pleted Transactions; later references are to the monthly Journal. 

Electrical World, New York. 

Engineering , London. 

Engineering Record, New York. 

Power (and the Engineer), New York. 

Stodola. Stodola's Steam Turbines; HE, Second Edition, in English, New York, 1905; IV, Fourth 
Edition, German, Berlin, 1910. 

Z.V.D.I., Zeitschrift des Vereine.s deutscher Ingenieure. 

Zeitschrift filr gesdmle Turbinenwesen. 



§ 48 (a)] 



TURBINE PERFORMANCE. 



479 



Table 20, page A — Continued. 



No. 



10 

11 

17 



18 
21 
22 



Various Notes. 



One wheel, 8.9 in. diameter, gear ratio about 10 to 1, vane speed 775 ft. 
per sec. at 2000 r.p.m. of power shaft. Superheat run to very high value, 
above range of practice. 

Eight impulse wheels, 24 in. diameter, vanes speed 293 ft. per sec. at 
2800 r.p.m. 

One 3- or 4-impulse wheel. 

One 3-impulse wheel, 25 in. diameter, vane speed 400 ft. per sec. at 
3600 r.p.m. 

One 3-impulse wheel, 36 in. diameter, vane speed 314 ft. per sec. at 
2000 r.p.m. 

The paper from which tests 2 to 5 are taken gives a good general descrip- 
tion and illustration of a number of small turbines. 

Machine similar in proportions to No. 1. See statement under Fig. 18, 
page 24, as to range of speed in De Laval turbines. 
Machine has one four-impulse wheel — see Fig. 352. 
Two three-impulse stages on one wheel, as in Fig. 352. 

Largest single-stage turbine ever built, and the only one of its kind. 
See Fig. 354 for form of buckets, which are of the tangential type: this 
particular machine has but one velocity stage. Wheel is 2 m. or 78.8 in. 
in diameter, and bucket velocity is 1030 ft. per sec. at 3000 r.p.m.; ma- 
chine has been run at 3800 r.p.m., as represented in Fig. 347. 

Same machine as is shown in Fig. 20; 24 one-impulse wheels, 20 to 33 in. 
diameter, vane speed 220 to 345 ft. per sec. at 2400 r.p.m. 

This machine is of the multistage type, generally similar to the Rateau 
and Zoelly turbines. 

The construction of this turbine is fully described in both the references 
given. See partial drawing in Fig. 365. 



Essential characteristics are very briefly stated; descriptive data 
vary so much in fulness that tabular columns cannot be made out for 
such things as wheel diameters and vane speed. For descriptions of 
form, refer to the illustrations in Chapters I and X, also to books on 
the turbine. 



Pages B, E. Operating Conditions and Steam Consumption. 

No. A serial number is given to each turbine; decimal figures denote 

different tests of the same turbine. 
Old This is the number of the particular test in the original 
No. report. Sometimes several original tests are here averaged 

together. 

(Go to page 483) 



480 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Table 20, page B. Tests of Various Steam Turbines. 



No. 


Old 

No. 


N 


H, K 


Pi 


h 


s 


Po 


s k 


K 


s h 


Qo 


1.1 




2014 


44h 


99.1 


327 





14.5 






. 39.53 


179.3 


2 




2354 


25h 


99.1 


654 


327 


14.5 






. 33.85 


179.1 


3 




2096 


51h 


99.3 


931 


604 


14.7 






. 25.68 


179.9 


2.1 




1000 


lOOh 


190 


378 





14.7 






. 62.3 


180 


2 




1600 


140h 


190 


378 





14.7 






. 45.8 


180 


3 




2800 


180h 


190 


378 





14.7 






. 37.3 


180 


3.1 


6 


1800 


23h 


105 


377 


46 


14.7 






. 47.1 


180 


2 


2 


2100 


24h 


105 


381 


50 


14.7 






. 44.0 


180 


3 


1 


2500 


26h 


105 


394 


63 


14.7 






. 41.9 


180 


4 




3600 


50h 


165 


366 





14.7 






. 32.0 


180 


5 




2000 


200h 


165 


366 





14.7 






. 28.0 


180 


6 




2000 


30h 


140 


353 





2.15 






. 22.0 


96.8 


7 




1635 


48h 


187 


376 





1.59 






. 21.9 


95.8 


8 




1076 


242h 


186 


407 


31 


2.28 






. 17.2 


99.0 


9.1 




751 


119h 


216 


388 


.022 


0.84 






. 16.77 


64.1 


2 




747 


333h 


221 


390 


.022 


1.67 






. 15.51 


87.6 


3 




750 


352h 


222 


475 


84 


1.47 






. 13.94 


83.1 


10 




3940 


12 


182 


505 


131 


1.28 4 


4.9 


.85 28.40 


78.2 


11 




2990 


205 


147 


357 





1.42 2 


6.3 


.89 17.42 


81.9 


12 




3000 


202 


201 


554 


172 


1.18 2 


2.44 


.89 14.91 


75.4 


13 




4990 


25 


95 


324 





0.59 2 


8.8 


.86 18.47 


52.8 


14 




5044 


53 


141 


354 





0.98 2 


8.0 


.87 18.18 


69.2 


15 




3640 


119 


115 


422 


84 


0.59 2 


4.3 


.88 15.95 


52.8 


16 




3028 


229 


140 


353 





0.98 2 


2.0 


.89 14.61 


69.2 


17.1 


12 


965 


210h 


66 


389 


89 


0.82 






. . 42.7 


63.3 


2 


14 


1770 


1114h 


183 


503 


128 


1.35 


> • • • 




. . 21.35 


80.1 


3 


5 


2941 


555 


116 


523 


185 


1.46 2 


2.13 


'.90 14.86 


82.8 


4 


7 


2993 


1334 


205 


554 


170 


2.19 1 


9.80 


.94 13.89 


97.6 


18.1 


4 


2184 


108 


176 


376 


5 


1.29 S 


0.42 


.84 19.06 


78.5 


2 


8 


2101 


366 


169 


388 


20 


1.64 2 


2.60 


.924 15.57 


87.0 


3 


12 


2360 


463 


224 


415 


24 


2.15 2 


2.09 


.933 15.38 


96.8 


19 


5 


1500 


1024 


179 


373 


.005 


2.43 2 


1.98 


.95 15.58 


101.4 


20 


1 


2613 


1050 


161 


581 


217 


1.18 1 


7.23 


.95 12.21 


75.4 


21 




1500 


1570 


182 


542 


168 


0.75 1 


6.47 


.94 11.54 


60.4 


22 


3,4 


3020 


327 


126 


611 


266 


0.49 1 


6.38 


.912 11.14 


47.0 


23 


4 


3000 


720 


203 


582 


199 


0.62 1 


5.09 


.920 10.36 


54.3 


24 


3,4 


3000 


1051 


164 


570 


205 


0.70 1 


4.67 


.916 10.02 


58.2 


25.1 


1 


1504 


1120 


198 


600 


219 


0.59 1 


5.44 


.905 10.42 


52.8 


2 


2 


1509 


1621 


205 


604 


220 


0.72 1 


4.60 


.926 10.10 


59.1 


3 


3 


1501 


2508 


198 


607 


226 


0.98 1 


4.11 


.950 10.02 


69.2 


26 


2,3 


1023 


5014 


170 


531 


163 


1.67 1 


6.16 


.953 11.47 


87.4 


27.1 




1500 


1750 


182 


544 


170 


0.53 1 


4.41 


.90 9.68 


49.5 


2 




1500 


3500 


183 


514 


140 


0.79 1 


4.09 


.95 9.98 


62.1 


28.1 




1815 


529 


165 


366 





1.00 1 


9.78 


.93 13.71 


69.8 


2 




1815 


515 


165 


656 


290 


1.00 1 


5.91 


.93 11.05 


69.8 



§ 48 (a)] TURBINE PERFORMANCE. 481 

Table 20, page C. Tests of Various Steam Turbines. 



h 


h 2 


Q 


Wr 


^h 




W k E h 


#Rh 


^Rk Qmh 


No. 


1186 


1046 


1007 


140.0 


64.4 




.064 


.457 


665 


1.1 


1353 


1166 


1173 


186.9 


75.2 




.064 


.402 


663 


2 


1488 


1255 


1308 


232.6 


95.5 




.073 


.411 


582 


3 


1198 


1012 


1018 


185.8 


40.8 




.040 


.220 


. . . 1055 


2.1 


1198 


1012 


1018 


185.8 


55.6 




.065 


.299 


656 


2 


1198 


1012 


1018 


185.8 


68.3 




.067 


.370 


628 


3 


1214 


1065 


1034 


148.2 


54.1 




.052 


.365 


812 


3.1 


1216 


1065 


1036 


150.7 


57.8 




.056 


.384 


761 


2 


1223 


1073 


1043 


149.4 


60.7 




.058 


.407 


730 


3 


1195 


1019 


1015 


176.2 


79.5 




078 


.451 


543 


4 


1195 


1019 


1015 


176.2 


90.9 




.089 


.515 


465 


5 


1193 


916 


1096 


277.0 


115.7 




.106 


.418 


402 


6 


1198 


889 


1102 


308.5 


116.2 




.105 


.377 


402 


7 


1217 


921 


1118 


296.2 


148.0 




.133 


.499 


318 


8 


1181 


867 


1120 


314.0 


151.8 




.135 


.483 


313 


9.1 


1182 


872 


1094 


309.4 


164.1 




.150 


.531 


283 


2 


1247 


911 


1163 


335.8 


182.4 




.157 


.543 


270 


3 


1273 


928 


1194 


344.7 


89.6 




76.0 .075 


.260 


220 565 


10 


1193 


895 


1112 


298.4 


145.9 


1 


29.7 .131 


.488 


434 234 


11 


1297 


930 


1222 


366.9 


170.7 


1 


51.8 .140 


.465 


413 303 


12 


1186 


872 


1133 


313.7 


137.9 


1 


18.5 .122 


.440 


378 348 


13 


1193 


880 


1124 


313.2 


140.0 


1 


21.9 .125 


.447 


389 340 


14 


1236 


894 


1183 


341.9 


159.5 


1 


40.3 .135 


.467 


411 314 


15 


1193 


880 


1124 


312.8 


174.0 


1 


55.1 .155 


.556 . 


495 274 


16 


1225 


936 


1162 


289.5 


59.6 




.051 


.206 . 


828 


17.1 


1271 


930 


1191 


341.4 


119.2 




.100 


.350 


424 


2 


1288 


971 


1205 


316.6 


171.3 


1 


54.2 .142 


.541 


487 299 


3 


1296 


963 


1199 


302.8 


183.5 


1 


72.2 .153 


.605 


568 277 


4 


1200 


885 


1121 


315.1 


138.6 


1 


12.0 .119 


.423 


355 356 


18.1 


1209 


905 


1122 


303.8 


163.5 


1 


50.9 .146 


.538 


497 291 


2 


1217 


907 


1120 


310.2 


165.5 


1 


54.4 .148 


.533 


498 286 


3 


1197 


913 


1095 


284.2 


163.6 


1 


55.2 .149 


.575 


546 284 


19 


1312 


954 


1236 


357.5 


208.3 


1 


98.0 .169 


.583 . 


554 252 


20 


1292 


913 


1231 


378.9 


220.3 


2 


07.0 .179 


.582 


547 237 


21 


1333 


932 


1286 


401.1 


228.6 


2 


08.4 .178 


.570 


520 238 


22 


1310 


906 


1256 


404.2 


245.9 


2 


26.1 .196 


.608 


560 217 


23 


1308 


923 


1249 


384.4 


254.2 


2 


32.6 .204 


.661 . 


605 208 


24 


1320 


910 


1268 


410.0 


244.3 


2 


20.9 .193 


.596 . 


539 220 


25.1 


1322 


919 


1263 


403.0 


252.1 


2 


33.7 .200 


.626 


580 212 


2 


1324 


938 


1255 


386.2 


254.5 


2 


41.8 .203 


.659 


625 209 


3 


1287 


954 


1200 


332.9 


222.0 


2 


11.2 .185 


.667 


635 229 


26 


1293 


896 


1243 


397.0 


263.0 


2 


36.6 .211 


.663 . 


596 201 


27.1 


1278 


906 


1216 


371.2 


255.0 


2 


42.1 .210 


.688 


653 202 


2 


1195 


872 


1126 


323.4 


185.6 


1 


72.5 .165 


.573 . 


533 257 


28.1 


1355 


963 


1285 


392.5 


230.2 


2 


14.2 .179 


.587 . 


546 237 


2 



I 



482 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 

Table 20, page D. Tests of Various Steam Turbines — Continued. 



No. 



Size, Make, Authority, Reference, etc. 



29 

30 
31 
32 
33 

34 



35 
36 

37 
38 
39 
40 

41 
42 
43 

44 

45 
46 

47 

48 

49 
50 



Turbines of Curtis Type— Continued. 

1000 kw. Thomson-Houston Curtis, 1000 r.p.m.; Engineering, 1907 II, 
Vol. 84, 375. 

Inm w r UT l- S ' lw ^^ r? "' 1 ?2&. I See Power, Dec. 20, 1910, 
8000 kw. Curtis, 750 r.p.m., Chicago, 1907; > oo- , ' , ' 

8000 kw. Curtis, 750 r.p.m., New York, 1908; ) ^ bL > als0 next page> 

9000 kw. Curtis, 750 r.p.m., Oakland, Cal., 1910; F. H. Varney, Jour. 

A.S.M.E., Dec. 1910, Vol. 32, 2089. 

450 kw. Schulz, M. F. Gutermuth, 1909; Z.V.D.I., 1910, Vol. 541, 82. 

Mixed-type Impulse Turbines. 

4000 kw. A.E.G. (German General Electric), Moabit Station, Berlin; 

Stodola IV, 399. 
4000 kw. A. E.G., Rummelsburg Station, Berlin, 1908; Zeit. fiirges. Turbin- 

enwesen, May 10, 1909; Z.V.D.I., 1909, Vol. 531, 761; Stodola IV, 

404. 

Reaction Turbines, Parsons and Variations. 

400 kw. Westinghouse-Parsons, 3500 r.p.m., Dean & Main, Pittsburgh, 
1903; F. Hodgkinson, Trans. A.S.M.E., 1904, Vol. 25, 716. 

5000 kw. Brown-Boveri-Parsons, 1000 r.p.m.; Essen, 1907; Stodola IV, 
449. 

7500 kw. Westinghouse-Parsons, 750 r.p.m.; New York, 1907; Electrical 
World, Dec. 14, 1907. 

4000 kw. Allis-Chalmers-Parsons; 1800 r.p.m.; R. C. Carpenter, Richmond, 
Va., 1908; Stodola IV, 467; also Sibley Journal of Engineering, 
Jan., 1911. 

3500 kw. Brown-Boveri-Parsons, 1350 r.p.m.; Frankfort; Z.V.D.I., 1908, 
Vol. 521, 516; Stodola IV, 449. 

3500 kw. Parsons, 1200 r.p.m.; Carville Station, Newcastle-on-Tyne; 
Engineering, 19071, Vol. 83, 654; Stodola IV, 439. 

6000 kw. Brown-Boveri-Parsons, 1200 r.p.m.; Mertz & McLellan, New- 
castle-on-Tyne; Engineering, 1911 1, Vol. 91, 314. 

Mixed-impulse and Reaction Turbines. 

500 kw. Melms-Pfenninger, 2500 r.p.m.; M. Schroeter, Munich, 1906; 

Z.V.D.I., 1906, Vol. 50 II, 1811, etc., Stodola IV, 481. 
2400 kw. Sulzer, 1500 r.p.m.; Paris; Stodola IV, 475. 
10,000 kw. Westinghouse Double-flow, 1800 r.p.m.; San Francisco, 1910; 

S. T. Naphtaly, Jour. A.S.M.E., Dec, 1910, Vol. 32, 2105. 

Low-pressure Turbines. 

300 h.p. Rateau, 1600 r.p.m.; Bruay, 1902; A. Rateau, Trans. A.S.M.E., 

1904, Vol. 25, 817; Stodola II E, 263. 
500 kw. Rateau, 1500 r.p.m.; Hallside Works, 1906; Engineering, 19061, 

Vol. 81, 848. 
600 kw. Brush-Parsons, 2000 r.p.m.; Engineering, 1910 II, Vol. 90, 8. 
5000 kw. Curtis, 720 r.p.m.; New York, 1909-10; H. G. Stott, R. J. S. 

Pigott, Jour. A.S.M.E., Mar., 1910, Vol. 32, 315. 



Note. — The heat quantities hi, h 2 , and Q in this table are the nearest integral 
approximations to calculated values with one decimal place. 



§ 48 (a)] 



TURBINE PERFORMANCE. 



483 



Table 20, page D — Continued. 



No. 



Various Notes. 



30 The Power reference contains summary of turbine tests, by Mr. G. A. 

31 Orrok, presented in discussion of A.S.M.E. papers describing tests of 

32 turbines here listed as Nos. 33 and 46. Only a few leading results from 
Nos. 30 to 32 have been published, in scattered fashion. The test of No. 
31 was very complete; perhaps the best summary of what has been made 
public will be found in Engineering, 1907 II, Vol. 84, 111. These are, 
presumably, all 5-stage machines; speed is either 750 r.p.m. with 25-cycle 
current or 720 r.p.m. with 60-cycle current. 

Horizontal machine, four 2-impulse wheels about 45 in. diameter; vane 
speed 435 ft. per sec. at 2200 r.p.m. See Fig. 348 for diagram and analysis 
of second test, and § 51 (o) for remark on scheme of regulation. 

35 Large turbines of this make have one or two Curtis wheels (2-impulse) 

36 followed by a series of single-impulse wheels. 
This turbine is made in two sections, like that shown in Fig. 20; low- 
pressure staging is especially complete, for full utilization of high vacuum. 

A series of single-impulse vane rows, mounted on the rotor drum instead 
of on wheels (see Fig. 355), is followed by reaction stage groups of the 
typical Parsons form. 

45 The general scheme of this turbine is well illustrated by Fig. 26. 

46 See Fig. 357 for general drawing of turbine. 

47 The turbine was installed for operation in conjunction with a Rateau 
accumulator — see § 50 (/) — but the test was evidently run with steam 
throttled from high pressure, as shown by the recorded superheat. 

Exhaust from several high-pressure engines was collected in an accum- 
ulator, where pressure ranged from 15 to 17 lb. absolute. As given in 
the first three tests, pi is the pressure below the governor valve, or at 
entrance to the first set of nozzles. Test 4 is the same as No. 3, but is 
worked out for the initial pressure above the throttle valve, with steam 
of the same initial total heat. 

Machine has eleven wheels, about 40 in. diameter; vane speed 260 ft. 
per sec. at 1500 r.p.m. 
49 Turbine fully described and illustrated in reference; double-flow arrange- 

ment, steam from ends to middle; mean vane-row diameter about 27 in., 
velocity about 240 ft. per sec. at 2000 r.p.m. 

Three two-impulse wheels, regular vertical turbine, condenser in base. 
Turbine in series with large engine, listed as No. 27 in Table 13. Only 
a separator (not very effective, apparently) between engine and turbine, 
so that pressures of engine exhaust and of turbine admission vary together. 
Very full data in paper, but see note under Table 25. Tests 1 to 4 represent 
series in which pressure between engine and turbine varied with load; 
while in tests 5 to 7 this pressure was held practically constant. 



{From page 479) 

N Speed in revolutions per minute : in many cases only the nominal 

speed is given. 

H Brake or effective horse-power: with the smaller machines, the 

load is expressed (and was measured) in this unit; such values, 
in the column under H and K, are marked by the letter h. 

Indicated horse-power, to be defined by analogy to the engine 
as the rate of work performance by the steam upon the vanes, 
is an imaginable quantity for the turbine; it may be calculated 

(Go to page 486) 



484 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Table 20, page E. Tests < 


of Various Steam Turbines. 


No. 


Old 
No. 


N 


H,K 


V\ 


k 


s, m 


Po 


<s k 


E e 


8 b 


9o 


29.1 




1000 


498 


168 


384 


16 


0.47 


19.4 


.90 


13.03 


45.8 


2 




(I 


1005 


168 


389 


21 


0.41 


17.0 


.94 


11.92 


41.7 


3 




u 


1005 


168 


466 


98 


0.41 


15.9 


.% 


11.15 


41.7 


4 




(( 


1275 


163 


508 


143 


0.47 


15.2 


.95 


10.78 


45.8 


30 




750 


5194 


180 


515 


142 


0.59 


13.52 


.97 


9.79 


52.8 


31 




750 


10816 


190 


525 


147 


0.25 


12.90 


.97 


9.34 


37.3 


32 




750 


8880 


193 


487 


109 


0.93 


15.05 


.97 


10.90 


67.4 


33 




750 


8775 


195 


453 


74 


0.97 


15.95 


.97 


11.53 


68.8 


34.1 


14 


2200 


83 


194 


539 


160 


1.41 


29.67 


.76 


16.81 


81.6 


2 


29 


2183 


447 


196 


543 


163 


1.39 


20.40 


.905 


13.77 


81.1 


3 


1* 


2104 


402 


188 


377 





1.25 


22.93 


.905 


15.47 


77.4 


35 




1500 


3206 


190 


646 


268 


0.68 


12.71 


.95 


9.01 


57.0 


36.1 


1,2 


1496 


2218 


198 


643 


262 


0.28 


11.85 


.93 


8.22 


30.5 


2 


3,4 


1500 


3243 


196 


629 


249 


0.28 


12.07 


.95 


8.55 


30.5 


3 


5,6 


1497 


4235 


194 


654 


275 


0.38 


12.08 


.96 


8.65 


39.4 


37.1 




3549 


594h 


170 


368 





1.46 






14.35 


82.8 


2 




3545 


594h 


169 


368 





0.99 






13.91 


79.5 


3 




3544 


593h 


165 


470 


104 


0.98 






12.50 


79.2 


4 




3543 


592h 


161 


544 


180 


0.93 






11.46 


67.4 


38 




1000 


5128 


176 


565 


194 


0.75 


14.32 


.94 


10.05 


60.4 


39 




750 


9865 


191 


474 


96 


1.32 


15.11 


.97 


10.94 


79.3 


40.1 




1800 


1393 


180 


450 


77 


0.82 


17.26 


.92 


11.85 


63.3 


2 




c i 


4328 


186 


484 


108 


0.84 


14.00 


.96 


10.03 


64.1 


41 




1350 


3522 


162 


498 


133 


0.55 


13.70 


.95 


9.70 


50.6 


42.1 


3 


1200 


2193 


217 


492 


103 


0.47 


14.52 


.925 


10.03 


45.8 


2 


7,8 


<< 


5112 


212 


493 


106 


0.43 


13.30 


.95 


9.43 


43.1 


3 


5 


a 


6222 


211 


503 


117 


0.51 


13.46 


.955 


9.60 


48.3 


43.1 




1200 


4256 


205 


546 


162 


0.40 


12.42 


.945 


8.76 


51.0 


2 




a 


5600 


204 


550 


166 


0.43 


12.12 


.955 


8.65 


53.1 


3 




a 


6257 


204 


560 


176 


0.44 


11.95 


.96 


8.56 


53.8 


44.1 


4 


2489 


147 


182 


583 


209 


0.37 


22.50 


.79 


13.28 


48.6 


2 


1 


2459 


499 


189 


607 


230 


0.50 


17.18 


.905 


11.60 


47.7 


45.1 




1500 


• 1200 


171 


569 


200 


0.62 


18.33 


.91 


12.46 


54.3 


2 




u 


2400 


171 


569 


200 


0.62 


15.28 


.93 


10.60 


54.3 


46.1 


1 


1800 


5333 


188 


431 


54 


0.82 


15.66 


.95 


11.10 


63.3 


2 


5 


it 


9173 


182 


433 


59 


1.03. 


14.57 


.97 


10.54 


70.8 


47 


5 


1598 


233 


14.7 


297 


85 


2.79 


39.97 


.94 


28.01 


106.7 


48.1 


1 


1500 


69 


2.90 


140 


.000 


0.58 


66.4 


.84 


41.65 


52.3 


2 


5 


it 


241 


6.11 


171 


.012 


0.74 


39.3 


.92 


27.00 


60.0 


3 


18 


a 


450 


11.40 


199 


.024 


0.98 


36.6 


M 


25.68 


69.2 


4 


18 


it 


450 


14.70 


212 


.029 


0.98 


36.6 


■ 94 


25.68 


69.2 


49.1 




2000 


306 


14.7 


212 


10 


0.52 


35.2 


.92 


24.19 


48.9 


2 


Mn. 


a 


600 


14.7 


212 


15 


0.87 


31.8 


.95 


22.54 


55.2 


50.1 


58 


750 


2213 


7.08 


177 


.043 


0.48 


36.85 


.92 


25.30 


46.4 


2 


60 


u 


4860 


12.10 


202 


.027 


0.43 


29.20 


.96 


20.93 


43.1 


3 


54 


u 


6283 


15.18 


214 


.031 


0.46 


28.11 


.965 


20.22 


45.1 


4 


38 


a 


7784 


20.60 


222 


.098 


0.74 


30.51 


.97 


22.08 


60.0 


5 


44 


a 


4426 


16.10 


217 


.079 


0.46 


27.72 


.958 


19.80 


45.1 


6 


42 


a 


4938 


16.24 


217 


.070 


0.65 


29.80 


.96 


21.35 


55.8 


7 


39 


it 


5895 


16.50 


218 


.106 


0.98 


31.75 


.965 


22.86 


61.7 



§ 48 (a)] 



TURBINE PERFORMANCE. 



485 



Table 


20, page F. 


Tests < 


df Various Steam Turbines. 


h 


h 


Q 


W R 


^h 


w± 


#h 


-#Rh 


•#Rk 


Qmh 


No. 


1206 


844 


1161 


362.8 


195.2 


175.9 


.168 


.538 


.485 


252 


29.1 


1210 


840 


1168 


369.5 


213.5 


200.5 


.183 


.578 


.543 


232 


2 


1253 


866 


1212 


387.4 


228.2 


214.5 


.188 


.589 


.554 


226 


3 


1276 


887 


1230 


389.0 


236.2 


224.5 


.192 


.607 


.577 


221 


4 


1278 


894 


1225 


384.6 


260.2 


252.3 


.213 


.677 


.656 


199 


30 


1282 


853 


1245 


429.2 


272.5 


264.4 


.219 


.635 


.616 


194 


31 


1262 


903 


1195 


359.1 


233.9 


226.7 


.196 


.652 


.631 


217 


32 


1234 


892 


1175 


351.3 


220.8 


213.9 


.188 


.629 


.610 


226 


33 


1289 


939 


•1208 


350.2 


151.3 


115.0 


.125 


.432 


.328 


339 


34.1 


1291 


939 


1210 


352.8 


184.8 


167.2 


.153 


.524 


.474 


277 


2 


1198 


877 


1120 


320.5 


164.6 


149.0 


.147 


.513 


.464 


288 


3 


1343 


931 


1286 


412.0 


282.4 


268.3 


.220 


.685 


.652 


193 


35 


1342 


885 


1311 


457.0 


309.4 


288.0 


.236 


.677 


.631 


180 


36.1 


1335 


882 


1305 


452.7 


297.6 


282.7 


.228 


.658 


.625 


186 


2 


1347 


903 


1308 


444.3 


294.0 


282.5 


.225 


.662 


.636 


189 


3 


1196 


889 


1113 


306.5 


172.4 




.155 


.563 




274 


37.1 


1196 


871 


1116 


325.1 


183.0 





.164 


.563 




259 


2 


1256 


911 


1177 


344.6 


203.7 




.173 


.591 




245 


3 


1295 


932 


1230 


363.0 


222.3 




.181 


.613 




234 


4 


1304 


921 


1240 


383.4 


253.3 


238.2 


.204 


.660 


.621 


208 


38 


1255 


916 


1176 


339.4 


232.7 


225.9 


.198 


.685 


.665 


214 


39 


1243 


888 


1180 


354.6 


215.0 


197.8 


.182 


.606 


.558 


233 


40.1 


1262 


899 


1198 


363.4 


254.0 


243.9 


.212 


.699 


.671 


200 


2 


1271 


892 


1220 


378.8 


262.1 


249.0 


.215 


.692 


.657 


197 


41 


1262 


863 


1217 


399.4 


253.9 


234.8 


.209 


.636 


.589 


213 


42.1 


1263 


861 


1220 


402.8 


270.0 


256.6 


.221 


.670 


.637 


192 


2 


1269 


872 


1221 


396.8 


265.0 


253.2 


.217 


.668 


.637 


195 


3 


1292 


875 


1241 


416.5 


290.2 


274.5 


.234 


.698 


.659 


181 


43.1 


1294 


879 


1243 


414.7 


294.2 


281.3 


.237 


.710 


.679 


179 


2 


1299 


883 


1246 


416.0 


297.5 


285.5 


.239 


.715 


.686 


177 


3 


1313 


889 


1264 


423.8 


191.7 


151.6 


.152 


.453 


.358 


280 


44.1 


1324 


907 


1277 


417.7 


219.3 


198.6 


.172 


.525 


.475 


247 


2 


1307 


914 


1252 


392.9 


204.3 


186.0 


.163 


.520 


.473 


260 


45.1 


1307 


914 


1252 


392.9 


240.0 


223.2 


.192 


.612 


.568 


221 


2 


1232 


879 


1168 


352.7 


229.2 


218.0 


.196 


.650 


.618 


216 


46.1 


1233 


892 


1163 


340.9 


241.3 


234.0 


.208 


.708 


.687 


204 


2 

^- 


1190 


1074 


1083 


116.2 


90.8 


85.4 


.084 


.782 


.735 


505 


47 * 


1121 


1024 


1069 


97.2 


61.1 


51.3 


.057 


.628 


.528 


740 


48.1 


1121 


994 


1061 


126.9 


94.3 


86.8 


.079 


.745 


.685 


537 


2 


1121 


971 


1052 


149.9 


99.1 


93.2 


.094 


.661 


.622 


452 


3 


1122 


937 


1052 


184.9 


99.1 


93.2 


.094 


.536 


.504 


452 


4 


1135 


960 


1086 


174.7 


105.2 


96.9 


.097 


.602 


.555 


438 


49.1 


1135 


959 


1080 


175.9 


113.0 


107.3 


.105 


.642 


.610 


405 


2 


1093 


937 


1046 


156.0 


100.6 


92.5 


.096 


.645 


.593 


442 


50.1 


1120 


924 


1077 


195.7 


121.7 


116.8 


.113 


.622 


.597 


375 


2 


1120 


915 


1075 


205.3 


125.8 


121.3 


.117 


.613 


.592 


362 


3 


1062 


875 


1002 


187.0 


115.2 


111.8 


.115 


.617 


.598 


369 


4 


1055 


876 


1010 


179.0 


128.5 


123.1 


.127 


.718 


.688 


334 


5 


1084 


899 


1028 


184.8 


119.2 


114.5 


.116 


.645 


.620 


366 


6 


1050 


888 


988 


161.3 


111.3 


107.5 


.113 


.690 


.667 


377 


7 



486 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 

{From page 483) 

by adding the friction work (both wheels-in-steam and bearing) 
as denned in § 47 (q) to the shaft output. This is not a practical 
determination, and is attempted only in special and highly 
detailed experiments. 

K . Load in kilowatts; all the larger machines were electrically 
loaded, and all values in the load column are in kilowatts unless 
marked h as just noted. 

Pi Initial steam pressure, above the throttle or control valve of 

the turbine, in pounds per square inch absolute. In one low- 
pressure turbine, No. 48, tests 1 to 3, which received steam at or 
a little above atmospheric pressure from a Rateau accumulator 
— see § 50 (/) — the initial pressure given is that below the 
governor valve. 

ti Initial steam temperature, measured at same place as pi, degrees 

fahrenheit. 

m Fraction of moisture in entering steam, if saturated. 

s Degrees of superheat of entering steam. 

p Exhaust pressure, preferably and presumably measured in ex- 

haust pipe of turbine; pounds per square inch absolute. 

$k Pounds of steam consumed per kilowatt-hour. 

E e Electrical efficiency of generator; when printed in italics, this 

has been assumed by author, at what seems a probable 
value. 

Sh Pounds of steam consumed per shaft or effective horse-power- 

hour: as shown in § 28 (e), page 279, 

S h =S k X (0.746 X E e ). ..... (240) 

qo Heat in one pound of feed water, which is taken to be at the 

temperature corresponding (as for saturated steam) to the ex- 
haust pressure p : see § 26 (e). 

Pages C, F. Thermodynamic Performance. 

hi Total heat of one pound of steam at pressure pi and of the quality 

fixed by m or s. 
hi Total heat at the end of adiabatic expansion from pi to p . 

Q Input of heat per pound of steam, equal to (hi — q ). 

IFr Output of the ideal Rankine cycle, in B.t.u. per pound of steam, 

equal to (hi — h%). 
TFh Actual work output per pound of steam, expressed in B.t.u., 

based on effective horse-power, and equal to (2545 -f- *Sh). 



48 (a)] 



TURBINE PERFORMANCE. 



487 



Wi 



E 



Work output per pound of steam, of turbine and generator com- 
bined, equal to (3412 + S k ). Evidently, 



W k ^ W h = E e 



(241) 



Absolute thermodynamic efficiency, based on effective horse- 
power, therefore equal to (W^ -r Q). 

i?R h Relative efficiency of turbine alone, equal to (TF h -f- TFr). 

E-Rk Relative efficiency of turbine and generator, equal to (W k -5- W-r) . 

Q mh Heat supplied per effective horse-power per minute, equal to 
(42.4 + E h ). 

(b) Discussion of Table 20. — Between turbines of different de- 
signs it is not well to draw close comparisons, unless much fuller data 
are available (as to both design and operation) than are generally made 
public — far more than are given in Table 20. It is thought, however, 
that the averaged results in Table 21 are valuable and instructive, as 
showing what has been attained by the best examples of the several 
types. The figures speak for themselves. 



Table 21. Thermodynamic Efficiencies of Various Types 
Turbines, with Generators, by Group Averages from 

Table 20. 



of 



Group. 


Load. 


St. Pr. 


Supht. 


Ex. Pr. 




Effici 


encies. 






K 


Pi 


s 


Po 


Eh 


Ellh 


#Rk 


Ee 


A 


2770 


178 


184 


1.04 


0.200 


0.666 


0.630 


0.955 


B 


8420 


176 


118 


0.66 


0.204 


0.647 


0.628 


0.97 


C 


3560 


186 


264 


0.45 


0.218 


0.668 


0.638 


0.955 


D 


5700 


193 


136 


0.73 


0.215 


0.687 


0.656 


0.955 


E 


9170 


182 


59 


1.03 


0.208 


0.708 


0.687 


0.97 



A. Zoelly turbine3, single-impulse wheels, tests 24, 25.3, 26, 27.2. 

B. Curtis turbines, two-impulse wheels, tests 30, 31, 32, 33. 

C A.E.G. (Curtis and Zoelly types combined), tests 35, 36.2, 36.3. 

D. Parsons type, many-stage reaction, tests 38, 39, 40.2, 41, 42.2, 43.2. 

E. Curtis and Parsons types combined, test 46.2. 

The tests selected for averaging are those near the rated power of the machine. 

For the same or similar turbines, it is of decided interest and im^ 
portance to see how efficiency varies with such governing conditions 
as size, load, steam pressure, steam quality, exhaust pressure, and speed; 
and these matters will now be taken up seriatim. In making compari- 
sons and forming judgment, the relative efficiency Er is by far the most 
useful criterion. 

(c) Influence of Size. — This is well represented by Fig. 339 
which shows how the ratio of actual to ideal output varies with rated 
power. The curve, sketched in by eye, is intended to serve as an 
approximate mean of the open-circled points belonging to the turbine 



488 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



alone, or derived from brake or shaft output. Naturally, with all kinds 
of machines represented, there is wide variation of points from curve, 
and the latter must not be given too high a standing as a law of relation. 



01 

0.6 

£r 
0.5 

0.4 

Fig. 339. — Influence of Size upon Relative Efficiency of Steam Turbines. Base 
electrical output K in kilowatts; ordinate, relative efficiency Er, from turbine 
output as i?Rh, from generator output as Er^. Points from turbines 11 to 
46 in Table 20, using tests at or near rated power. 

One thing to be noted is that above 3000 to 4000 kw. capacity size 
apparently ceases to have any influence upon economy. 

(d) Influence of Load Factor. — Figure 340 shows how the rela- 
tive efficiency falls off with decrease of load, but continues to increase as 
the load goes above rating. In the latter characteristic the turbine 





y 


O ^- 


"ft 







• 




n 


• o 

• 




--. "j 


o 

0, 




o 




• 
o 


• 


■ t 


9 






• 




o 

• 


/ 

o r « 


— / 

O 

• 


• 








°=E Rh 








•J 

/ 


r * 
































































• 


20 


00 K 


w. 40 


00 




6000 


8000 


10000 





































I.I 

1.0 

0.9 

0.8 

0.7 






















-r--° 


o 






XL. 












< 


^, 


( 


<r — ~ 

i 





















/ 

/ 


x 

s* 


























/ 
/ 
/ 

/ 


/ 
o 


























( 


) 





2 





4 





6 





3 


1 





1. 


2 


L 


4 





Fig. 340. — Variation of Efficiency with Load Factor. Base, ratio of actual elec- 
trical load to rated load; ordinate, ratio of relative efficiency E^ at the par- 
ticular load to that at rated load. Data from turbines 25, 27, 29, 34, 40, 42, 
and 43 in Table 20. 

differs from the piston engine, which at once begins to lose efficiency 
when overloaded — in the two types of machine rating bears about 
the same ratio to maximum capacity. The examples here represented 
are much fewer than in Fig. 339, and again the curve sketched in as a 
rough mean has little more than illustrative value. One turbine, ]STo. 36, 



§ 48 (d)} 



TURBINE PERFORMANCE. 



489 



is intentionally omitted, because it follows the opposite law of an in- 
crease of Er with decrease of load: this is due to the extremely low 
exhaust pressure, and will receive fuller comment in Art. (h). 



100000 

STEAM 
PER 

Hour 




7000 

Fig. 341. — Comparison of an Engine and a Turbine, as to Variation of Steam 
Consumption with Load. Engine, 42 and 86 by 60 in. duplex compound, rated 
5000 kw., No. 27 in Table 13, page 268. Turbine, 5000 kw. Zoelly, No. 26 in 
Table 20. Base is electrical output in kilowatts; ordinate shows total pounds 
of steam per hour to scale at left, also pounds per kilowatt-hour to scale formed 
by inclined lines — compare Fig. 87, etc., in Chapter V. 

The contrast between characteristic steam-consumption curves for 
engine and for turbine is well illustrated in Fig. 341. The engine tests 
do not run low enough to give a good comparison at light loads; but 
whereas the two machines are in practical agreement from 3000 to 
4000 kw., the steam rate S^ of the turbine continues to decrease as the 
load rises, while that of the engine passes a minimum and then increases 
quite rapidly. 
14 




Kw. 5000 10000 15000 

Fig. 342. — Steam Consumption of 8000 Kw. Curtis Turbine, No. 31 in Table 20. 

Figure 342 is a simple plot of steam rate on output for a large tur- 
bine: it shows that S k , after slowly falling to a minimum, rises rather 
abruptly with heavy overload. Just how such an overload is carried 



490 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



depends upon the method of governing, or upon the "valve gear" of 
the turbine — see § 52. The scheme of bypassing the first stages, 
throwing them more or less completely out of action, seems most likely 
to give a definite and decided rise in steam consumption at high 
loads. 

(e) Influence of Steam Conditions. — The three elements of 
initial pressure, initial quality, and exhaust pressure are closely linked 
together. Concerning these, experience with steam turbines has crystal- 
lized into certain general conclusions or opinions which have almost, 
if not quite, the standing of. fundamental principles. After these have 
been stated, they will be discussed with the help of the data in Table 20. 

1. The turbine works more effectively at the low-pressure than at 
the high-pressure end of the operation of expansion; in other words, 
the losses from ideal effect are greater with high steam density than 
with low density. 

2. Superheat is very beneficial, diminishing steam friction and 
greatly reducing steam consumption. 

3. The turbine can effectively receive and apply the energy made 
available by lowering the exhaust pressure, hence high vacuum is de- 
sirable and economical. 

To give a general view of information along this line, the plot in 
Fig. 343 is made from Table 20, using rated-load results from the large 



0.7 
0.6 


• 


1 










• 
• 








• 




• 
•• 

• 
• 

• 

• 
• 


• 

• 
> 










• 
• • 




■ 

• 

• 


• 
• 
• 

• 


•• 

• 
• 


• 
• 


A 










SB 

• 
• 

• 
• 




C 

» 


• 

• 
• 

58< 

i i i Inn 


•• 

1 , 1 il 








i 


o ° < 

— M c 

1 1 II lllllll 


3 


.-* 




4 






i 


A 


P>. 


0.5 










IC 


)0 


t 2C 


)0 


De 


:g. 


3C 


)0 Fa 


HR. 4( 


)0 


5( 


)0 


6( 


)0 



Fig. 343. — Efficiency in Conversion of Energy, as related to range of steam pressure 

and of superheat. 



and medium-size turbines The relative efficiency by turbine output, 
2?Rh, is measured vertically, to the scale at the left. On each line like 
ABC thus located are laid off to the base scale, first, at A, the exhaust 
temperature t as taken from Table I for p ; next, at B, the saturation 
temperature corresponding to pi; lastly, at C, the actual initial tern- 



§ 48 (e)] TURBINE PERFORMANCE. 491 

perature. The two circled dots under B show tests in which there was 
no superheat. 

As might be expected, with data from various kinds and sizes of 
turbines, there is no sign of any law of relation between the steam 
conditions and efficiency. It is therefore necessary to fall back upon 
the few cases in which conditions were varied with the same turbine. 
Two of these are given in the diagram, where the dotted inclined lines 
connect points from the same machine, and show moderate improvement 
as the result of superheating. 

(/) The Question of Pkessure Range. — Comparing the low- 
pressure or exhaust-steam turbines in Table 20 with those of full range, 
we note a decided advantage in relative efficiency for the low range. 
The stage efficiencies in the example in Table 24, Art. (k), although 
somewhat erratic in their manner of variation, also help to confirm 
statement 1 in the last article. 

Low efficiency in the upper stages is readily accounted for by greater 
steam friction and by greater leakage. Experiments on rotor resistance 
have shown that surface friction is just about proportional to steam 
density. As to leakage, there is much more room for this in drum-rotor 
turbines than in those having a series of wheels in chambers separated 
by diaphragms. Some clearance between running and standing parts 
is always necessary, and the greater the diameter of the running joint 
the greater the opening for leakage. At the high-pressure end of a 
reaction turbine especially, clearance area will bear a high ratio to the 
small channel area between short vanes. 

The poorer working of the turbine at high pressure is a strong argu- 
ment for the combination of high-pressure engines with low-pressure 
turbines — see the results from a large combined unit set forth in Art. 
(m). The advantage is scarcely great enough to justify the higher cost 
of the double system in a new plant for electrical service; but it is all 
in favor of increasing the capacity and economy of existing engine plants 
by adding low-pressure turbines. 

(g) Effect of Superheating. — A number of comparative tests 
without and with (or with varying degrees of) superheat are collected 
in Table 22; these are from small and medium-size turbines, since the 
tests of big machines have all been run with superheated steam, except 
in low-pressure operation. The actual gain in thermal efficiency E^ 
is not nearly so great as the apparent improvement in steam consump- 
tion S&; but except where the type of construction limits capability of 
getting the full benefit of increased steam velocity (tests 1, 11, 12), 
there is a gain in relative efficiency Er^. No remarkable benefit from 
superheating is apparent; and it may well be questioned whether a 



492 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Table 22. Turbine Tests Showing Effect of Superheating. 



No. 


Load. 


Pi 


Po 


s 


s h 


E b 


•^Kh 


Type. 


1.1 

3 


44 h 
51 h 


99 
99 


14.5 
14.7 



604 


39.5 
25.7 


.064 
.073 


.457 
.411 


De Laval. 


9.2 
3 


333 h 
352 h 


221 

222 


1.67 
1.47 




84 


15.5 
13.9 


.150 
.157 


.531 
.543 


De Laval. 


11 
12 


205 k 
202 k 


147 
201 


1.42 
1.18 



172 


17.5 
14.9 


.131 
.140 


.488 
.465 


Elektra. 


28.1 
2 


529 k 
515 k 


165 
165 


1.00 
1.00 



290 


13.7 
11.1 


.165 
.179 


.573 

.587 


Curtis. 


29.2 
3 
4 


1005 k 
1005 k 
1375 k 


168 
168 
163 


0.41 
0.41 
0.47 


21 

98 

143 


11.9 
11.2 
10.8 


.183 

.188 
.192 


.578 
.589 
.607 


Curtis. 


34.3 
2 


402 k 
447 k 


188 
196 


1.25 
1.39 



163 


15.5 
13.8 


.147 
.153 


.513 

.524 


Schulz. 


37.2 
3 
4 


594 h 
593 h 
592 h 


169 
165 
161 


0.99 
0.98 
0.93 



104 
180 


13.9 
12.5 
11.5 


.164 
.173 
.181 


.563 
.591 
.613 


Parsons. 



For meaning of symbols, see Art. (a). 

maximum in overall economy, or in commercial efficiency, is not reached 
at a lower degree of superheat than is given in many of the tests in 
Table 20. 

The absence of valves and pistons obviates most of the operating 
difficulties which arise from the use of superheated steam in the engine: 
there remain the danger of burning out the tubes of the superheater, 
more trouble with steam piping, and greater temperature distortion of 
the turbine. Against these lie the advantages of lower steam friction 
and (reported) less wear of vanes by dry, gaseous steam. As a summary 
of the examples in Table 22, and with other less purely technical data 
in mind, it may be stated that a thermal gain of 7 to 10 per cent (in 
absolute efficiency E h ) and a commercial gain of perhaps 4 to 6 per cent 
is about all that can be expected from the use of superheated steam: 
while with excessive superheat the cost efficiency of the whole plant 
(counting in depreciation and repairs) may fall below the maximum 
attainable. 

In contrast with high-pressure practice, note how wet was the steam 
supplied to low-pressure turbine No. 50, Table 20: this was in spite of 
a separator intended to remove water from the engine exhaust. 

(h) Effect of Vacuum. — Of comparative tests in which exhaust 
pressure was the principal variable, but few can be selected from Table 



§ 48 (h)] 



TURBINE PERFORMANCE. 



493 



20; and of the first two pairs in Table 23, Nos. 26 x and 34 x are not given 
in the main table. Test 26 x appears on Fig. 341 in an abnormally low 
point, hence the apparent gain cannot all be credited to greater vacuum. 

Table 23. Tests Showing Variation of Vacuum. 



No. 


Load. 


Pi 


s 


Po 


«h 


E h 


•#Rh 


26 
26 x 


5015 
5141 


170 
166 


163 
176 


1.67 
1.20 


11.47 
10.75 


.185 
.195 


.667 
.674 


•34.2 
34 x 


447 
396 


196 
191 


163 
189 


1.39 
0.80 


13.77 
13.20 


.153 
.155 


.524 
.501 


37.1 
2 


594 
594 


170 
169 






1.46 
0.99 


14.35 
13.91 


.155 
.164 


.563 
.563 


36.1 
2 
3 


2218 
3243 
4235 


198 
196 
194 


262 
249 
275 


0.28 
0.28 
0.38 


8.22 
8.55 
8.65 


.236 

.228 
.225 


.677 
.658 
.662 



14 



12- 



For meaning of symbols, see Art. (a). 

The essential deduction from Table 23, from a wider view of test 
data, and from rational considerations, is that a particular turbine 
cannot follow, with undiminished relative efficiency, a lowering of the 
exhaust pressure below the value for which the machine was designed. 
Load and rate of steam flow remaining nearly the same, the last stage 
or stages will get more energy and higher steam velocities as the vacuum 
is greater; but with a fixed vane speed 
these higher velocities cannot be fully 
utilized. 

If the efficiency ratio Er were main- 
tained constant by the machine, a plot 
of steam rate S^ on exhaust pressure p - 
would give a curve like AB, Fig. 344; 
but instead of thus falling off at an in- 
creasing rate as p is less, the steam con- io 
sumption per power unit follows very 
nearly a straight line like AC. If p * 
rises above the best value, line CA will 
be produced upward, showing a falling off in En with excessive back 
pressure. 

The last test group in Table 23, No. 36, is an interesting example 
of a turbine with more vacuum than it can effectively utilize, at least 
at full load. With half load, less steam admitted, and lower stage 
pressures, the last stages have less excess of energy and the general 



















A 








C/ 












b/ 












) 


Po 


Ll 


3. 2 


> 


3 



344. — Variation of Steam 
Rate with Exhaust Pressure. 



494 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



efficiency ratio is better than at full load : this accounts for the apparent 
departure from the usual relation exhibited in Fig. 340. Test 31 is 
another case of excessive vacuum with consequent low value of Er. 
Beside lowering the relative efficiency, this condition may be carried so 
far as to pass the limit of increase of absolute efficiency E, in a manner 
analogous to that set forth for the engine in Fig. 128. 

(i) Influence of Speed. — Continuing the discussion in § 46 (g), 
we now consider the question of how working efficiency is affected by 
change from normal action, which is shown as case I in Fig. 345, where 



W U A 




^mim* 




Fig. 345. 





«\\ 




Various Speeds with the Same Vanes. 



the short parallel lines above and below the vane profiles indicate rela- 
tive directions of steam flow. At II, as the extreme of underspeeding, 
the vanes are held fixed; then with the assumption of no bucket loss, 
represented by making Yi equal Vi, no kinetic energy would be ab- 
stracted from the jet — but compare § 47 (n), under Observations of 
Pressure. At III the vane speed T is so large that absolute exit velocity 
V is inclined in the same general direction as jet velocity V; further, 
account is taken of bucket loss, in that V2 is made less than V\. From 
the profile diagram it appears that poor entrance conditions, with the 
jet striking the approaching, convex side of the vane, will tend to aug- 
ment the secondary losses. 

Steam turbines are not likely to be run above their designed speed; 
but relative overspeeding, essentially equivalent to case III of Fig. 345, 
occurs when the jet velocity is much diminished at light loads, in ordinary 
constant-speed machines. Underspeeding, with resulting loss in the 
form of residual kinetic in the jet at exit from the vanes, is a trouble 
belonging rather to marine service. 

(j) Speed and Energy Losses. — By experiment it has been found 
that the friction of steam on metal surfaces varies about as the square 
of the relative velocity, ranging from the 1.8 to the 2.0 power. For 



§ 48 (j)] 



TURBINE PERFORMANCE. 



495 



rotor friction, this resistance is multiplied by speed to get power ab- 
sorbed, so that the latter varies nearly as the cube of revolutions per 
minute. This fact tends to lower the speed of maximum efficiency 
from the ideal value deduced in § 46 (g), most strikingly *in a noncon- 
densing impulse turbine with a number of wheels and consequently a 
large amount of moving surface. 

The effect of speed change upon energy losses is well illustrated by 
the experiments represented in Fig. 346. This simple turbine was 
especially adapted to feeling and showing the effect of speed alone, as 
an independent variable; in a more complex machine, change of speed 



100 
80 
60 

40 

7o 
20 



-Radiation 



















7 


►■II. 

- NOZZLE 


































' 


' 
















































































-Bucket 

i i 




































-Residual 












































































l Fr 


ICT 


ON 


AL 










































































U< 


5EH 


JL 










































































* 


' 























2000 



N 



2500 R.rm. 3000 



3500 



Fig. 346. — Results from a Large Single-stage One-impulse Riedler-Stumpf Turbine 
No. 17 in Table 20. Experiments and deductions by F. Rotscher, Zeit. Ver. 
deutsch. Ing., 1907, Vol. 51 1. One wheel 78.8 in. in diameter, normal speed 
3000 r.p.m. Initial pressure 200 lb. abs., superheat 125 deg. fahr., exhaust 
pressure 1.3 lb. abs. 



will involve some change in other conditions, such as stage pressures. 
Useful output was measured as shaft horse-power, nozzle and frictional 
losses were found by separate experiments, and the remainder was 
apportioned among bucket and residual-velocity losses by inference. 
The best relative efficiency attained in this series of tests, even at 
3800 r.p.m., is quite a little below that in test 17.4, Table 20, where the 
speed was only 3000 r.p.m. but "the exhaust pressure was higher. Natur- 
ally, a much abbreviated turbine such as this will not be capable of 
utilizing high vacuum (or low exhaust pressure) to good effect. 

(k) Performance by Stages. — A typical temperature-entropy 
diagram for the steam turbine is given in Fig. 347, using an example 
with comparatively few stages. The whole available energy, area 



496 



ACTION OF THE STEAM IN THE TURBINE. [Ghap. IX. 



A1B1CE4, is divided into four equal parts by the lines A2B2, A3B3, A 4 B 4 . 
Let the relative efficiency in each stage be 0.65, and in stage 1 draw line 
G1H1 to divide area A1B1C1E1 in the ratio 0.65 to 0.35: then A1G1H1E1 
represents the useful energy given to the wheel and G1B1C1H1 is the 
total waste. Assuming zero radiation, the latter is all supposed to be 
returned to the steam at the pressure of line A 2 B 2 , increasing its entropy 
by the amount CiB 2 . The available energy for the second stage is 
now A2B2C2E2, and G2H2 is drawn so as to cut off 0.65 of this in A2G2H2E2. 
The final result of applying the efficiency 0.65 in every stage is to make 
the area between A X E 4 and the GH lines equal to 0.685 of A1B1CE4: 
and the excess of this ratio over the mean of the partial ratios shows 
the gain resulting from the return of energy not utilized in the early 
stages. 



200=i 



1003 

P 



= -800 



-700 



,0 i 

5- 



I- 




G 3 



H, 



H, 



--600 



G A 




a 



N 



1.0 




Fig. 347. — Temperature-entropy Diagram for a Four-stage Turbine: pi = 165 lb. 
abs., steam initially dry-saturated, p Q = 1 lb. abs. 



It must be clearly understood that the GH lines in Fig. 347 are not 
lines of operation, or do not represent any operation within the turbine : 
each of them simply sets off an area equivalent to that part of the ideally 
available energy which, as the result of very complex secondary actions, 
is not usefully applied in driving the rotor. 

(I) The Mollier Diagram. — The heat-entropy or Mollier dia- 
gram — see general description in § 18, page 138 — is by far the best 
scheme of representation for turbine performance. An illustrative 
example, worked out with data from an actual test, is diagrammed in 
Fig. 348 and given numerically in Table 24. The turbine has four two- 



§ 48 (l). 



TURBINE PERFORMANCE. 



497 



impulse stages and is essentially similar to the Curtis machine in Fig. 23; 
but it is much smaller and is horizontal instead of vertical. A special 
feature is the control (by hand) of the number of nozzles open for 
passage of steam in the three diaphragms between wheels. 

In Fig. 348, line 1A represents adiabatic expansion in the first 
nozzles and A2 shows the return at p 2 of all the energy not usefully 
applied. Horizontal line 2K divides the ideal heat drop or available 
energy 1A into realized output IK and return KA. The succeeding 



1300 




Fig. 348. — Mollier Diagram from 450 Kw. Four-stage Schulz Turbine, Test 34.2 
in Table 20. Steam per brake horse-power-hour, Sh = 13.77 lb.; work output 
per pound of steam, W = 184.8 B.t.u. Other data, with calculated quantities 
in Table 24. 

stages are similarly represented by 2B3L, 3C4M, and 4DON. In 
stage 1, dotted line 1H shows the probable actual expansion in the noz- 
zle, with some loss of energy in friction, etc. ; it is drawn for 10 per cent 
nozzle loss, or the vertical height from A to H is one-tenth of Al. For 
the whole expansion, 1G, GO, and OP show what would be an equivalent 
effect in ideal jet formation, heat return, and resultant efficiency: heat 
IP is the useful output and 1P/1G the efficiency ratio. 

The values in Table 24 are all calculated from the steam tables, 
but in practical use of the Mollier diagram (in service form) they would 
be found graphically. A highly essential feature of this test is the fact 



498 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



that the steam is superheated at the points 2, 3, and 4, or at entrance 
to the second, third, and fourth sets of nozzles. If these stage points 
lay below the saturation line SS, their positions would be indeterminate : 
that is, the heat content of the steam at entrance to the stages would 
be unknown, and could be found only by the use of some sort of steam 
calorimeter. No determinations of this sort for wet steam in turbine 
stages have as yet been made, or made public. 

Table 24. Observed and Calculated Quantities for Turbine 
Test Represented in Fig. 348. 



Quantity. . 


Whole 
cycle. 






Stage. 






l 


2 


3 


4 


1. Pressure 

2. Temperature. 

3. Sat. temp. . . . 

4. Superheat. . . 

5. Total heat. . . 

6. Entropy 


.pi ... 

.h.... 
..t a .... 

.s . . . . 

.hi... 
. .n. . . . 


1 

1 
1 
1 
1 
1 


190.5 
543.0 
377.8 
165.2 
1291.9 
1.6525 


l 
l 
l 
l 
l 
l 


190.5 
543.0 
377.8 
165.2 
1291.9 
1.6525 


2 
2 
2 
2 

2 

2 


54.0 

415.4 

285.9 

129.5 

1240.7 

1.7326 


3 
3 
3 
3 
3 
3 


20.05 
332.6 
228.1 
104.5 
1205.8 
1.7991 


4 
4 
4 
4 
4 
4 


5.83 

206.6 

168.8 

37.8 

1150.1 

1.8580 


7. Actual 

8. Output 


hi . . . 
W... 



IP 


1104.8 
187.1 


K 
IK 


1240.7 
51.2 


L 
2L 


1205.8 
34.9 


M 
3M 


1150.1 
55.7 


N 
4N 


1104.8 
45.3 


9. Ideal 


.h 2 .... 


G 
1G 


940.0 
351.9 
0.532 


A 
1A 


1175.2 
116.7 
0.439 


B 
2B 


1156.7 

84.0 

0.416 


C 
3C 


1113.1 

92.7 
0.601 


D 
4D 


1057.7 

92.4 

0.490 


10. Output 

11. Rel. eff 


■W R .. 

E R .. 



Small figures and letters at left edge of each column refer to Fig. 348. 



The calculations for Table 24 involve no new points, unless, perhaps, 
in the idea of measuring actual heat content at the common state of 
exit from one stage and entrance to the next; and they are illustrated 
in the example which follows. Terminal point O is in the wet-steam 
region, and must be located indirectly. A note under Fig. 348 states 
that the output per pound of steam, based on brake horse-power, is 
184.8 B.t.u. Work used up in friction of wheels in steam is properly a 
part of the heat returned; but purely mechanical friction is altogether 
outside of steam action. As very moderate allowance for bearing 
friction and governor resistance, If per cent is added to 184.8, making 
the net steam-work output 187.1 B.t.u. Measured down from 1, this 
locates the division point P on 1G, and the intersection of constant-heat 
line PO with constant pressure line GO fixes the terminal point O, for the 
whole cycle and for stage 4. A minor inaccuracy in the general scheme 
of the diagram is the disregard of radiation; but the amount of heat 
involved in this action is relatively very small. 



§ 48 (Z)] TURBINE PERFORMANCE. 499 

Example 51. — Make calculations for the third stage in Fig. 348 and 
Table 24, and get the abscissa of terminal point 0. 

The first operation is carried out as in Example 49. With pressure pi = 
20.05 lb. abs. and temperature ti = 332.6 deg., total heat hi is read from Table 
VII as 1205.8 B.t.u. and entropy n from Table VIII as 1.7991; the latter locates 
line 3C, also, at pressure p 2 = 5.83 lb., fixes . moisture m 2 as 0.0198 and total 
heat h 2 as 1113.1. For the same pressure 5.83 lb. and the observed temperature 
206.6 deg. (in the column for stage 4), total heat by Table VII is 1150.1 B.t.u. 
Now actual output is W = 1205.8 — 1150.1 = 55.7, and ideal output is Wr = 
1205.8 - 1113.1 = 92.7; then relative efficiency E R is 55.7 -r- 92.7 = 0.601. 

To get point O, we have that final heat content h = initial heat 1291.9 — 
output 187.1 = 1104.8 B.t.u. At the exhaust pressure 1.39 lb., total heat 
H = 1109.3 and latent heat r = 1028.4; then a heat deficiency of the value 
1109.3 — 1104.8 = 4.5 corresponds with the moisture fraction m = 4.5 -s- 1028 
= 0.0044. With JV = 1.9481 and b = 1.7957, the final entropy is n = 1.9481 
- (0.0044 X 1,7957) = 1.9481 - 0.0079 = 1.9402. 

(m) The Combined Unit. — The combined working of a high- 
pressure engine and a low-pressure turbine is well represented by the 
tests set forth in Table 25. In a few points this workup differs from 
that compressed into Table 20. The same idea is followed of changing 
from generator output to shaft power, even though the electrical effi- 
ciency of the generator must be assumed; but here the real turbine 
output is left in kilowatt measure, in lines 5 to 7. All work and energy 
quantities are related to one pound of steam entering the engine, hence 
to less than one pound of that entering the turbine: the exact relative 
weight of the turbine steam is given in line 20. This scheme makes the 
heat received by the turbine, line 36, exactly comparable with that 
rejected by the engine, line 35; the difference (around 40 B.t.u. in the 
last three tests, greater in the first) is lost in radiation and in the hot 
water drained from the engine receiver and from the intermediate 
separator. 

The relative efficiency of the turbine, while fair, is below that of 
several smaller machines which precede it in Table 20. This may be 
due to excessive moisture in the steam flowing from the separator to 
the turbine. As in all the examples worked out in this book, initial 
heat content is calculated for actual steam quality: that is, heat hi in 
line 36 is for a steam-and-water mixture containing the water fraction 
w t in line 21; but it is for less than one pound of that mixture, as has 
just been stated. The engine shows an excellent relative efficiency, 
due to large size and small thermal losses in the cylinders — refer to 
remarks under Fig. 137, page 256. 

In absolute efficiency this combined unit is equaled by turbines 
27, 30, 31, 40, 41, 42, and 46 in Table 20, and is surpassed only by 



500 



ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 



Table 25. Combined Working of Engine and Turbine, Capacity 
16,000 Kw., Interborough Power House, New York. 



Original test number , 
Number in Table 20. 
Number in Table 13 . 
Diagram in Fig. 137 . 



1. 
2. 
3. 
4. 

5. 
6. 

7. 

8. 

9. 

10. 

11. 
12. 
13. 

14. 
15. 
16. 



17. 
18. 
19. 
20. 
21. 
22. 



23. 
24. 
25. 
26. 

27. 
28. 
29. 
30. 



31. 
32. 
33. 
34. 
35. 



36. 
37. 
38. 
39. 



POWER AND WORK OUTPUT 

Generator ) engine K e . 

output ) turbine. K t . 

Electrical I engine 

efficiency \ turbine 

Shaft i engine K se . 

output [ turbine K s t . 

in kw. ; unit K s . 



Steam ) to engine . . . 
per > drained out 
hour ) to turbine . . 



Steam per ) engine 
shaft kw. ' +"T-Kir«, 
per hour 



• • • $ke . 

/ turbine #kt • 

) unit Sb. 



Output ) engine We 

per pound > turbine Wt 

of steam ) unit W . 

STEAM CONDITIONS 

Initial press, abs pi. 

Initial quality mi. 

Intermediate pressure. . . .pi . 

Steam to I weight 

turbine ) quality mt. 

Exhaust pressure p . 

WHOLE UNIT 

Initial heat content. 
Ideal final heat. . . . 
Exhaust-feed heat. . 

Ideal output 

Relative efficiency. . 

Input of heat 

Absolute efficiency. 
By experimenters . . 



Hi.. 
A*. 

go . 

W* 

E R 
Q.. 

E.. 
E'. 



Engine Alone 

Initial heat hi.. 

Ideal final heat hz. . 

Ideal output W n 

Relative efficiency E R 

Heat from engine 



Turbine Alone 

Initial heat hi.. 

Ideal final heat hi. . 

Ideal output W n 

Relative efficiency. ..... .E n . 



44 
50.5 

27.2 
B 



4940 
4426 
0.960 
0.958 
5150 
4620 
9770 



131080 

8390 

122690 

25.48 
28.40 
13.42 

133.9 
120.1 
254.0 



198.8 
0.013 
16.10 
0.9360 
0.079 
0.46 



1187.5 

821.4 

45.1 

366.1 

0.693 

1142.4 
0.222 
0.211 



1187.5 

1007.4 

180.1 

0.743 

1053.6 



987.4 
819.8 
167.6 
0.717 



60 

50.2 

27.3 

C 



6923 

4860 

0.967 

0.960 

7155 

5055 

12210 



159760 

17830 

141930 

22.32 
31.60 
13.08 

152.8 
108.0 
260.8 



195.1 
0.010 
12.10 

0.8883 

0.027 

0.43 



1189.8 

820.6 

43.1 

369.2 

0.707 

1146.7 
0.227 
0.218 



1189.8 
991.8 
198.0 
0.773 

1037.0 



994.7 
820.8 
173.9 
0.622 



54 
50.3 



7820 

6283 

0.972 

0.965 

8040 

6510 

14550 



195745 

19180 

176565 

24.35 
30.03 
13.44 

140.2 
113.6 
253.8 



193.4 
0.011 
15.18 
0.9020 
0.031 
0.46 



1188.8 

823.4 

45.1 

365.4 

0.695 

1143.7 
0.222 
0.212 



1188.8 

1005.3 

183.5 

0.764 

1048.6 



1010.6 
825.4 
185.2 
0.613 



38 
50.4 



8384 

7784 

0.975 

0.970 

8600 

8030 

16630 



244905 

7425 

237480 

28.52 
30.52 
14.74 

119.7 
111.8 
231.5 



197.0 
0.005 
20.60 
0.9697 
0.098 
0.74 



1193.9 

843.1 

60.0 

350.8 

0.660 

1133.9 
0.205 

•0.195 



1193.9 

1027.7 

166.2 

0.720 

1074.2 



1029.8 
848.5 
181.3 
0.617 



kw. 
kw. 

a 
a 

lb. 
it 

it 

lb. 

a 

B.t.u. 
tt 

it 

lb. 

lb 

ft 

lb. 

B.t.u. 

a 

tt 
ti 

B.t.u. 
B.t.u. 

a 
tt 

B.t.u. 
B.t.u. 



§ 48 (w)] TURBINE PERFORMANCE. 501 

NOTES ON TABLE 25. 

Engine 42 and 86 by 60 in. duplex compound, rated 5000 kw., No. 27 in Table 13. 
Turbine 5000 kw. 3-stage Curtis, No. 50 in Table 20. H. G. Stott and R. J. S. 
Pigott, Jour. A.S.M.E., Mar., 1910. Only primary data used in workup, as noted 
below; derived quantities, notably water rates, are inconsistent in original report. 

Notes on Items. 

I, 2, 8, 9, 10, 17, 18, 19, 21, 22; from original tables of data. 

3, 4; assumed at probable values, to change basis of efficiency to shaft output. 

5, 6, 7; shaft output, or power delivered to generator, but expressed in kilowatts 
instead of horse-power. 

9; Water drained from engine receiver and from intermediate separator; note how 
a low value of this quantity corresponds with a high value of moisture in steam to 
turbine, line 21. 

II, 12, 13; these are all from total steam to engine or to plant, line 8. Rates 
marked "Actual" in Table 12 of original report are really dry-steam rates, with 
simple subtraction of entrained water. 

14, 15, 16; divide 3412 by £ k to get W; see § 26 (c). 

20; weight of steam going to turbine, per pound of steam to engine, or line 10 
-J- line 8. 

21; this mt is fraction of water in steam to turbine. 

23, 31; for one pound of steam, at pressure in line 17 and quality in line 18. 

24; calculated for adiabatic expansion to exhaust pressure po in line 22. 

25; heat in feed water, if at temperature corresponding to po. 

26, 27, 28, 29; same meaning and methods as in Table 20; actual output W in 
line 16. 

30; as derived in original report, from actual electrical output and hot- well tem- 
perature. 

31, 32, 33, 34; same meaning and methods as in Table 20, actual output W e in 
line 14; first two tests are in Table 13, but performance is there worked for indicated 
instead of. shaft horse-power. 

35; whole heat rejected by engine, or initial heat hi in line 23 or line 31 less 
engine output W e in line 14. 

36, 37, 38; taken from Table 20, but diminished to correspond with weight of 
steam entering turbine (per pound of initial steam), as given in line 20. The value 
of Wt in line 15 bears this same ratio to that of W in Table 20. 

Nos. 36 and 43. This result is attained without superheat, and with 
wetter steam going to the turbine, even after the drainage of 5 to 10 
per cent of water, than would go to the lower stages of the high-super- 
heat turbines. In spite of these handicaps, the relative efficiency of 
the plant, line 27 of Table 25, is in the region of the best attained by 
the turbine alone under the most favorable conditions. 

With the engine for efficient utilization of the high-pressure end of 
the cycle and the turbine for the low-pressure end, and with both 
machines designed from the beginning for combined operation, the most 
economical steam plant possible can undoubtedly be evolved. A rela- 
tive efficiency of 75 per cent — or, with the regenerative feed-heating 
scheme, of 80 per cent — does not seem an extravagant prediction for 
big units. Whether the advantage of the piston engine over the high- 
pressure stages of the turbine is enough to overbalance its higher first 
cost, carrying thermal gain over into the column of resultant gain in 
total cost, is another question, not to be gone into here. 



i 



502 ACTION OF THE STEAM IN THE TURBINE. [Chap. IX. 

(n) Estimate of Turbine Losses. — A review of the column for 
relative efficiency 2?Rh in Table 20, with Fig. 339, will show that the 
combined losses in turbines from 1000 kw. rating upward ranges from 
0.40 to 0.30 of the available energy. Of this, about one-sixth is probably 
nozzle loss and another sixth may be lost in residual velocity and rotor 
friction, leaving the remaining two-thirds as bucket loss (including the 
effect of leakage). This statement is, of course, a mere approximate 
summary of empirical knowledge. To rationalize the waste actions in 
the turbine is at least as difficult a problem as to rationalize the thermal 
action of the cylinder walls in the engine — and is as far from complete 
solution. Much effort has been expended in the attempt to develop 
a mathematical theory of steam friction : it is well established, as stated 
in Arts. (/) and (j), that surface friction is about proportional to steam 
density and to the square of velocity; but even if these were rigid laws, 
their application to conditions of rapidly changing density and velocity 
would be exceedingly complicated. This task is the less worth while 
because of the large relative magnitude of the wholly indeterminable 
effect of steam shock, eddy currents, etc.; under " steam shock" may 
be included such variations of pressure within vane channels as are 
described in § 47 (w). 

There are several good reasons why a formulation of empirical infor- 
mation on the detail of steam action in the turbine — analogous to 
that made for the engine in §§ 22 to 25, Chapter V — should not be 
attempted here. The body of information is as yet but fragmentary, 
although a good deal has been published in the last few years, especially 
from German sources;* the subject is decidedly one for the specialist 
in turbine design rather than for the general power engineer; and it 
belongs properly to a large and full treatise such as that of Stodola, not 
to a textbook for engineering students. 

In brief summary of the last two sections of this chapter, it may 
be stated that the ideal jet as worked out in § 16 will be modified in 
the actual nozzle to the extent of 5 to 10 per cent; while the " theoretical" 
bucket action in § 46, in respect to the effective performance of work, 
fails of realization by as much as 25 to 40 per cent. The larger the 
vanes and the easier their curves, the smaller will be the losses, both 
by surface friction and by secondary dynamic actions. 

* Statement written in summer of 1911. 






CHAPTER X 
DESIGN AND CONSTRUCTION OF THE TURBINE 
§ 49. Design for Steam Action 

(a) Dimensions of Steam Channel. — In laying out an engine 
which shall develop a certain power, the principal step is to determine 
proper sizes for the cylinders, and the machine is then built up around 
these volumes. The analogous fundamental determination in the de- 
sign of a turbine is that of the channel (through nozzles and buckets) 
along which the working current will flow. The essential requirements 
are that this channel be of the right size to carry the necessary amount 
of steam, and that it be properly graded in sectional area so as to per- 
mit and produce correct expansion of the steam. We shall here go no 
farther than this primary design for steam action. 

Having given initial pressure and state of steam and exhaust pres- 
sure, the ideal output per pound is to be calculated for the Rankine 
cycle as in § 15 (d), or read from a Mollier diagram: the method of cal- 
culation is more clearly illustrated in Example 49, page 469, than in 
Example 15, page 105. Then the assumption of a probable relative 
efficiency will lead to the actual work per pound of steam; and from 
this, with the desired power of the turbine, the total steam per hour, 
minute, or second is readily found. The simplest case is that of the 
single-stage, one-impulse turbine, which is little more than a nozzle 
problem. 

Example 52. — Assuming ideal steam action, find (A) the combined nozzle 
area for a 300 brake horse-power turbine, with dry saturated steam at 150 lb. 
abs. and an exhaust pressure of 1.5 lb. abs. Then see how the capacity of this 
turbine will be affected by (B) change to steam with 10 per cent of moisture 
and (C) to steam with 150 deg. of superheat. 

First get the ideal output in all three cases, as follows : 

Case A 

1. Initial total heat, h 1193.8 

2. Entropy, adiabatic expansion, n . . 1.5697 

3. Dry-steam entropy at p , or N 2 . . 1.9417 

4. Entropy shortage, N 2 - n = An . 0.3720 

503 



B 


c 


1107.4 


1277.3 B.t.u 


1.4642 


1.6640 


1.9417 


1.9417 


0.4775 


0.2777 



B 


c 


1.7846 


1.7846 


0.2674 


0.1555 


835.8 


950.8 B.t.u 


271.6 


326.5 " 



504 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

Case A 

5. Entropy of vaporization at p , or b 2 . 1.7846 

6. Final moisture fraction, m 2 . . . 0.2085 

7. Final total heat, h 2 896.5 

8. Ideal output, Wr 297.3 

9. Now assume a relative efficiency of 0.55; then the output per pound of 

steam in case A will be W = 297.3 X 0.55 = 163.5 B.t.u. 

10. The steam per horse-power-hour will be Sh. = 2545 -r 163.5 = 15.56 lb. 

Then for 300 h.p. the total steam will be 4670 lb. per hour or 1.298 lb. 
• per sec, say 1.3 lb. 
Next, calculate the throat dimensions of a unit ideal jet for each initial con- 
dition, being guided by Fig. 65 in choosing the throat pressure. 

Case A B ' C 

11. Pressure at throat of jet, p t . . . 87.0 88.0 86.0 1b. 

12. Dry-steam entropy, N t 1.6135 1.6126 1.6144 

0.0380 0.1291 53.7 

1149.7 1068.4 1223.6 B.t.u. 

44.1 39.0 53.7 " 

1484 1410 1640 f .p.s. 

4.862 4.355 5.609 cu. ft. 

0.472 0.445 0.492 sq. in. 

70.8 66.8 73.8 



13. Steam quality at p t , mors 

14. Heat content &t p, or h t . . 

15. Energy in jet, hi - h t = W t . 

16. Velocity of jet, V t , by Eq. (104) 

17. Specific volume, v t . . . . 

18. Area of throat, a 

19. Napier divisor, D = a pi . . 

20. Since the turbine requires 1.3 lb. of steam per sec. in case A, and the throat 

area of the unit jet is 0.472 sq. in. (this can be read from Table 7 also), 
the total least cross area of the nozzles must be 0.472 X 1.3 = 0.613 
sq. in. The ideal rate of energy availability is 1.3 X 297.3 = 386 B.t.u. 
per sec. 

21. In case B the area just fixed will discharge 0.613 ■*• 0.445 = 1.378 lb. of 

steam per second, of which the available energy will be 1.378 X 271.6 = 
374 B.t.u. Relative efficiency will probably be less with wet steam, 
so that the power of the turbine will be about 5 per cent less than in 
case A. 

22. In case C, the steam flow will be 0.613 ■*• 0.492 = 1.2460 lb., which will 

have an available energy of 1.246 X 326.5 = 407 B.t.u. It appears 

therefore that the use of superheated steam will increase the power of a 

turbine with given nozzles. 

This example carries forward the investigation of Fig. 65. There it was 

found that rate of flow increased with wet steam, decreased with superheat, for 

a given orifice area : now we see that these effects are overbalanced by changes 

of available energy (per pound) with initial steam condition. We have not 

taken into account the coefficient of discharge, as discussed in § 47; this would 

slightly modify the absolute rates of steam flow, and might make a small change 

in their relative size. 

(b) The Multistage Turbine. — Suppose that a turbine has a 
number of equal stages, with the same kinetic energy and velocity of 



§ 49 (6)] 



DESIGN FOR STEAM ACTION. 



505 



the steam at the mouth of each successive set of nozzles. Then the 
area of channel in each stage, in nozzles and through vanes, will be 
directly proportional to the specific volume of the steam, at the con- 
dition in which it leaves the nozzles. This volume is shown by the re- 
spective lengths GiHi, G 2 H 2 , etc., in Fig. 349; where the stepped curve 
BC corresponds with the outline BiCiB 2 ***C 4 in Fig. 347, and BD 
with the plain adiabatic BiC. For equal stages, areas ABHiGi, 
GiHiH 2 G 2 , etc., in Fig. 349, will be equal to each other; and, as just 
stated, the nozzle areas will bear the same ratio to the volumes GiH^ 
G 2 H 2 , etc. With unequal stages, this ratio will change; if the energy 




o 1 « — — V 

Fig. 349. — Pressure- volume Diagram for a Multistage Turbine. 

and steam velocity of the stages are increased, the cross area required 
for steam flow will be relatively less. The successive enlargements of 
lotor diameter in a reaction turbine like Fig. 25 are in accord with this 
principle. 

Quantitatively dependent upon entropy relations, the pressure-vol- 
ume diagram as in Fig. 349 is of little or no use for primary determina- 
tions, whether of stage pressures or of jet dimensions. Its purpose is 
wholly illustrative: and in pursuance of that idea, the line of constant 
total heat is drawn in curve BF, while S is a point on the saturation 
curve from B. 

To divide the original ideally available area A1B1CE4, Fig. 347, into 
equal parts (or in some other definite manner) is a comparatively easy 
task; but the return of unused heat from the higher stages disturbs the 
proportions of such an initial division. The stage areas A1B1C1E1, 
A2B2C2E2, etc., can be equalized only by a very ' troublesome cut-and- 
try adjustment of the heights of lines A 2 B 2 , A3B3, etc., or of the stage 



506 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

pressures. The Mollier or heat-entropy diagram, already exemplified 
in Fig. 348, is far more useful and convenient for this kind of determina- 
tion than is the plain temperature-entropy diagram. 

(c) Use of the Mollier Diagram. — Drawn for illustrative pur- 
poses, Fig. 350 is made much clearer and more open than the service 
diagram : only the lines of constant pressure are put in (with one quality 
curve in the saturation line SS); and these are spaced for pressures 
corresponding to each ten degrees of saturation temperature, as in Fig. 
72. With the steam limits named, line AB represents the operation of 



1300 




Fig. 350. — Diagram for Four-stage Turbine, working from 180 lb. abs. and 150 deg. 

of superheat to 1 lb. abs. 



ideal jet formation and application. The relative efficiency being taken 
as 0.60, AC is made equal to 0.6 of AB; then intersection of the hori- 
zontal or constant-heat line CD with the exhaust-pressure line BD 
locates the final state point at D. 

As has been indicated, the solution of the problem of dividing the 
whole work performance in a desired manner among the stages con- 
sists in fixing the intermediate stage pressures. Obviously, division of 
the length AB into four equal parts would be equivalent to a similar 



§ 49 (c)] DESIGN FOR STEAM ACTION. 507 

division of the area A1B1CE4 in Fig. 347; and locations with reference 
to the pressure and temperature lines of Fig. 350 could be transferred 
directly to the temperature axis of Fig. 347. This scheme of division 
will, however, give a larger energy value to the lower stages, as has 
already been pointed out. 

If equality of the stage energies, represented in Fig. 350 by the 
vertical lines from AG or 1 to HL or 4, be desired, the problem has no 
simply definite solution. The individual stage diagrams, like AGFE 
and HLDK are generally similar to the overall diagram ABCD; but 
even with a fairly simple expression for the constant-heat lines in terms 
of the coordinates of the diagram, relations among the stage quantities 
would be rather complex. Lacking such a foundation for mathematical 
determination, it is necessary to fall back on the cut-and-try method; 
although with the advantage that it is easier to handle heat and energy 
as linear quantities, than as areas in the original temperature-entropy 
diagram. Before going farther with this particular problem of stage 
equalization, we will consider a purely graphical scheme, which is out- 
lined in Fig. 350. 

(d) The Stage-point Locus. — In that diagram, the useful out- 
put AC is spaced off into four equal parts, implying the same net work 
performance in all the stages. From the division points horizontal 
(dotted) lines are extended toward the right, until they meet the stage- 
point locus AD. The example shows the result of using a straight line 
For this locus: in the clear space at the bottom of the figure are laid out 
:he lengths of the stage energies AG to HL, divided into output AE to 

[K and returned heat EG to KL. The numbers in the lines are rela- 
tive efficiencies, from AE/AG = 0.51 to HK/HL = 0.60. Some such 
increase of relative efficiency with fall of pressure is highly probable — 
compare statements in § 48 (/) and showing of Fig. 348 — even though 
the exact results in the diagram are not likely to be realized. 

In further illustration of the scheme just described, Fig. 351 shows 
the partition of the same total output into ten stages, of which the last 
four are together equal to the first six. The upper half of AC is divided 

Lto six twelfths, the lower half into four eighths, and the stage points 
are again determined by a straight-line locus AD. In the group of 

lorizontal parallel lines representing the stage energies, lengths from 
the main diagram are doubled. 

The simplest way to modify the stage quantities, while preserving 
reasonable and consistent relation among them, is to substitute a 
slightly curved line for the straight locus AD: this will be concave 

ipward, or will sag below AD, and will be used with the same skeleton 
)f horizontals, from the same division points on AC. The shape of 



508 



DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 



curve that would, for instance, equalize the stage or nozzle energies 
(like AG to HL, Fig. 350) cannot be definitely formulated, since it will 
change in form with the positions of A and D. Approximation by 



1300 




1.7 

Fig. 351. 



Ji 1.8 

— Diagram for Ten Stages. 



.9 



trial is still necessary, but the operation has now as little as possible of 
the random element. 

(e) Form of the Mollier Diagram. — If the constant-pressure 
lines were parallel, the scheme of Fig. 350 would make all the stages 
alike, establishing a constant ratio of output to jet energy. Since the 
entropy gained with a certain amount of heat is less as the temperature 
is higher, the lines of constant pressure rise with increasing steepness. 
This makes them diverge from left toward right; and the growth, with 
higher steam quality, of the vertical distance between any pair, repre- 
sents the increase in energy available for conversion into work. The 
same increase is shown in Example 52; but the diagram, once drawn 
with sufficient accuracy, greatly surpasses numerical calculation in 
convenience. 

(/) Proportions of Turbine Stages. — One or the other of the 
ideas just set forth — either to equalize or in some other ratio to relate 
the jet energies, or to aim at a similar relation among net outputs — 
will naturally govern turbine design. As between the two schemes, 
there is probably little to choose in the matter of overall efficiency. 
The stage pressures having been decided upon, nozzle areas will be cal- 
culated by the methods of Example 52, with the help of the volume 
lines when using a Mollier diagram. 

Only with a comparatively small number of stages in the turbine 



§ 49 (/)] DESIGN FOR STEAM ACTION. 509 

will divergent nozzles be required. The minimum number for straight 
nozzles may be determined, roughly, by applying the relation expressed 
in'Eq. (144), page 287, letting R and r stand for ratios of pressures 
rather than of volumes. This relation R = r n is strictly true only with 
the expansion curve pv = C; but as appears from Fig. 349, the resultant 
curve BC does not depart very greatly from the equilateral hyperbola. 
Suppose that in a turbine with expansion from 150 lb. to 1 lb. abs. the 
number of stages is to be such that in each the pressure ratio (of high 
to low pressure) shall not exceed 1.7, the reciprocal of 0.58. Then we 
have R = 150, r = 1.7, whence n = log 150 -*■ log 1.7 = 2.176 -f- 0.230 
= 9.5. Since it is better to err on the side of deficiency of divergence 
— see § 47 (/) and last paragraph of (m) — we may have as few as 
eight equal stages without using divergent nozzles. 

As to the control of stage pressure, in design or in operation, it will 
be raised by decreasing the opening through succeeding nozzles, lowered 
by increasing that opening. This is closely analogous to the effect of 
shorter and longer cut-off upon a preceding receiver pressure in a mul- 
tiple-expansion engine. Generally the nozzle openings, after the first, 
are fixed and unchangeable; but sometimes, as in the Schulz turbine of 
which a test is diagrammed in Fig. 348, there is control (by hand) of 
the lower sets of nozzles. 

To consider a different type of staging, suppose that a group of 
stages has a uniform channel area running through it, as is true of 
several groups in Fig. 25. With fall of pressure and increase of specific 
volume, steam velocity must be greater for equal flow rate. The stage 
pressures will therefore adjust themselves so as to give smaller energy 
values to the upper stages, larger values to the lower stages. In other 
words, pressure will be backed up throughout the group, its gradient 
running higher than for equal stages. Obviously, such interrelation of 
stages will be a component in the control of stage pressure as described 
in the last paragraph. 

(g) Proportions of Vane Channels. — The sectional profiles of 
vanes or blades, especially the edge angles, will be governed by velocity 
diagrams as laid out in § 46 (d), (/), (j), and (I), with modification of 
impulse vanes by the considerations set forth in Fig. 337. As to effec- 
tive width of channel, the relations in § 46 (k) are very little affected by 
the secondary departures from ideal action. In impulse turbines, the 
depth of channel or length of vanes is made equal to or a little greater 
than the diameter of nozzle mouth: with several velocity stages, of the 
Curtis type, the vane lengths are progressively increased, as noted in 
§ 46 (n) and shown in Fig. 360. In the reaction turbine, length of vane 
is one of the main dimensions of the cross area which determines flow. 



510 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

§ 50. Various Forms of the Turbine 

(a) Types of Steam Action. — Concerning this matter, little or 
nothing is to be added to the classification on page 32; a notable fact is 
the strong tendency existing toward a combination of the Curtis and 
Parsons types, as exemplified in Fig. 26 and in Fig. 357. 

The condensed body of descriptive matter now to be given is 
in continuation of and in addition to the general description in § 4> 
Chapter I. 

(6) Directions of Steam Flow. — All the turbines illustrated in 
§ 4 have what is called axial flow, through nozzles and vanes as well as 
in general direction. A glance at flow conditions, with the more defi- 
nite showing of Fig. 323, makes apparent the fact that the steam path 
through a series of stages is really helical in form. With partial periph- 
eral admission, Figs. 19 and 22, there must be considerable sidewise 
spreading or circumferential flow of the steam current in the wheel 
chambers. 




Fig. 352. — The Elektra -Turbine, Radial-flow, Two-stage, Three-impulse: much 

structural detail omitted. 



Figure 352 is an example of radial flow, alternately inward and out- 
ward through one ring of vanes. This design has the merits of com- 
pactness and, for a several-impulse type with return to the same vanes, 
of definite guidance of the steam current after its first velocity stage: 



§ 50 (&)] 



VARIOUS FORMS OF THE TURBINE. 



511 



** 



but the wide and long guide channels seem to favor the formation of 
eddy currents. Some early Parsons turbines, in the experimental stage, 
had radial flow; and several recent designs of small reaction turbines 
show a return to this scheme, largely for the sake of compactness. 

The method of tangential flow is 
illustrated in Figs. 353 and 354, the 
first with buckets of the Pelton form, 
adopted from the impulse type of water 
wheel. The use of two parallel wheels 
or bucket rows in one stage (at the 
left side of Fig. 353) is only a tenta- 
tive suggestion, not carried out in prac- 
tice because the steam currents would 
interfere in escaping from the buckets and flowing to the next nozzles. 

A full development of the idea of semicylindrical buckets, milled from 
the solid metal of the wheel rim, is shown in Fig. 354: the milling cutter 




Fig. 353. — Elementary Sketch of 
the Kerr Turbine. 



WFm\ 




Fig. 354. — Working Elements of the Riedler-Stumpf Turbine. 

is of the same form that would be used for making a straight T slot, and 
is so held as to give the plane of the bucket an angle of 15° or 16° with 



512 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 



a plane tangent to the rim. Nozzle positions with single and double 
rows of buckets are indicated at II, where the second sketch represents 
the single-impulse arrangement of the large one-stage turbine listed as 
No. 17 in Table 20. The other drawings illustrate schemes of velocity 
staging, with peculiarly curved return channels or guide passages. At 
III we have simple return to the same single row of buckets: Fig. 312 
shows the need for different angles (with wheel rim) at entrance to and 
•at exit from the guide channel G. Drawing IV shows a similar return 
of the split current discharged from the first velocity stage on a double- 
row wheel. The scheme at V, with separate, larger buckets for the 
second velocity stage, permits closer spacing of the buckets along the 
circumference of the casing. 

The manufacture of this turbine, never carried very far, has been 
given up (by the Allgemeine Elektricitats Gesellschaft), in favor of de- 
signs with ordinary radial vanes. Several small turbines built in this 
country, as the Terry and Sturtevant, are similar in principle to scheme 
III in Fig. 354, but for return channels have fixed buckets in the casing 
similar to those in the wheel — see the paper, " Small Steam Turbines," 
by Mr. G. A. Orrok, Trans. A.S.M.E., 1909, Vol. 31, 263, reprinted in 
Power for May 11, 1909. 

(c) Variations of Impulse Turbines. — Among this class there is 
scarcely any essential departure from the type of arrangement shown in 
Figs. 20 and 23, with the wheels in chambers separated by diaphragms. 
Horizontal machines have these partition discs split on a diameter, each 

half being fast in its part of the casing; but the 
Curtis turbine has solid diaphragms, which must 
be put in place when the wheels are being as- 
sembled • on the shaft, then handled with the 
rotor when the machine is put together. 

The one radical departure from " normal" 
construction is to mount impulse vanes on a 
drum (as in the reaction turbine) and have the 
fixed nozzle rings make a running fit (as close 
as practicable) with the rotor. The sketch in 
Fig. 355, which gives no detail of the blade 
fastenings but merely indicates their overall ■ 
bulk, shows two out of a considerable group 
Impulse Stages, f single-impulse stages at the high-pressure 
bine. en d of the Melms Pfenninger mixed-type tur- 

bine; the rest of the machine is of Parsons type, 
with reaction vanes on the same drum The plane " joint " between 
nozzle-vane ring and rotor runs with a clearance of about 0.01 in. 



1 



B 



S 




§ 50 (c)] 



VARIOUS FORMS OF THE TURBINE. 



513 



A similar group of single-impulse stages on a' broad wheel or short 
drum forms the low-pressure end of the Oerlikon-Rateau turbine; and 
in the marine Curtis turbine — see Art. (g) — the last three or four 
3-impulse stages are thus mounted on one wheel. With the latter type 
of staging only the nozzle rings, not the intermediate guides, need run 
close with the rotor. 

(d) Variations of Reaction Turbines. — Starting with the typi- 
cal Parsons arrangement shown in Fig. 25, the first important change 
has been in the balance discs or pistons: Fig. 356 shows the quite largely 




Fig. 356. — Section of Rotor and Casing, 8000 Kw. Tosi-Parsons Turbine, to illus- 
trate Fullager system of balancing and construction of rotor. Stodola IV, 
450; Power, Oct. 13, 1908. Scale 1 to 42. 



used Fullager system. Pistons Pi and P 2 remain as before, but the 
large P 3 of Fig. 25 is replaced by the smaller P 3 in Fig. 356, at the other 
end of the rotor. The net area of this P 3 is equal to the annular area of 
step 3, at D; then the remainder of the right-hand end of the rotor is 
balanced by carrying the condenser pressure over to the outer face of 
P 2 . This plan requires much less enlargement of the casing for the 
balance discs; and inside of one " stuffing box" (at the right) the steam 
pressure is not far from atmospheric, so that liability to air leakage is 
much diminished. In Fig. 356, regular admission is at A, and under 
heavy overload steam is bypassed to B. 

The introduction of one or two initial, high-pressure stages of the 
Curtis type not only replaces the small-area reaction stages in which 
leakage is of serious magnitude, but also makes easy an arrangement 
which is more or less self-balanced — see Fig. 26. The double-flow 
system, represented by Fig. 357, still further facilitates the elimination 
of end thrust. 

A good description of various forms of the Westinghouse double-flow 
turbine will be found in Power for June 16, 1908; all of them have flow 



514 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 



^^^^^\\S\\\\\\\\\\^ 




o 



,0 



CO 

6 

> OS 

o v 

.as 

13 ^ 

^ r 

CD <U 

.1-1 r ^ 
-Q - 

3S 
002 

a» S 

co p 

bD 





CO 

6 
1— < 

fa 



§ 50 (d)] VARIOUS FORMS OF THE TURBINE. 515 

from the middle toward the ends, thus requiring two stuffing boxes 
tight against leakage of air into the condenser, just as in Fig. 25. 
For low-pressure service, the impulse stages are naturally omitted; 
then flow from the ends toward the middle, as in the Brush-Parsons 
turbine, No. 49 in Table 20, reduces the danger of air leakage to a 
minimum. 

(e) Low-pressure and Mixed-flow Turbines. — The low-pres- 
sure turbine differs in no essential particular from the lower stages of the 
same type of full-range machine. If the supply of engine exhaust is 
irregular or intermittent, provision must be made for feeding the tur- 
bine directly from the boiler. The simplest method is to pass live steam 
through a reducing valve, cutting it down to the normal admission 
pressure of the turbine. A reaction turbine must be operated in this 
way, unless a special group of high-pressure stages, commonly running 
idle, is provided. But an impulse turbine may, more simply, have an 
extra set of high-pressure nozzles, of small throat area; then even 
though the jet from these has too high a velocity for full utilization at 
the established vane speed, a good part of the energy that would other- 
wise be wasted in pure throttling is recovered. 

(/) The Rateau Accumulator. — To make the exhaust-steam 
turbine effective in sequence with a group of noncondensing engines 
somewhat irregular in operation, Professor Rateau invented his " ac- 
cumulator." This is a storage vessel or tank in the steam line between 
engines and turbine, designed to hold heat, not steam. In some cases 
it has been filled with heavy slabs or discs of cast iron, but more com- 
monly there is a tier of iron troughs, which stand full of hot water at 
about 212 deg. If the steam supply is less than the demand by the tur- 
bine, stored heat will be given off, with evaporation of water and some 
fall of temperature and pressure. An excess of exhaust will restore heat 
to the accumulator, raising temperature and pressure until an auto- 
matic relief valve comes into action. Complementary to the latter, 
there must be a bypass from the boiler, to supply reduced steam in 
case of a prolonged deficiency of exhaust. 

(g) The Marine Turbine. — As remarked on page 32, the most 
trying requirement imposed on designers of marine turbines is that of 
comparatively low speed, for the sake of propeller efficiency: in some 
recent large installations turbine speeds have been made less than 
200 r.p.m., in contrast with the very common 750 r.p.m. which is a 
minimum for big turbogenerators. To accommodate the necessarily 
large number of stages, Parsons turbines are commonly made in sec- 
tions; quite often, one high-pressure and two low-pressure turbines are 
on three shafts, the latter two with reversing rotors; while the biggest 



516 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

ships have a complete duplex arrangement, with four shafts. Under 
the Curtis system, enough stages can easily be put into one casing. 
Leading particulars from a few large ships will suffice here. 

Large Marine Turbine Plants. 

1. Steamships Lusitania and Mauretania. Engineering, 1907 II, 
19081, Vols. 84, 85. Four Parsons turbines, two high-pressure, two 
low-pressure. High rotor drum, 96 in. diam., vanes 2.5 to 12 in. long; 
low drum, 140 in. diam., vanes 8 to 22 in. long. Steam pressure 210 lb. 
abs., speed about 190 r.p.m.; vane speed, at mid-length, 80 to 130 ft. 
per sec. About 60 stages in low-pressure section, twice as many in 
high-pressure. Combined rating, 70,000 h.p. 

2. Steamships Olympic and Titanic. Power for July 11, 1911, etc. 
One low-pressure Parsons turbine, working from 9 lb. abs., in sequence 
with two reciprocating engines. Rotor 12 ft. diam., vanes 18 to 25.5 
in. long; speed 165 r.p.m.; vane speed, at average mid-length, 120 ft. 
per sec. Rating, engines 30,000 h.p., turbine 16,000 h.p. 

3. U. S. battleship North Dakota. Power, May 25, 1909. Two 
Curtis turbines, 25,000 h.p. total; steam pressure, 280 lb. abs., reduced 
to 75 lb. abs. in first stage; speed, 245 r.p.m. Wheels about 12 ft. diam. 
to mid-length of vanes, latter 1.8 to 12 in. long; vane speed about 
155 ft. per sec. 

(h) The Geared Turbine. ■ — If high machine efficiency, quiet 
running, and durability can be secured, the use of toothed gearing be- 
tween turbine and propeller will greatly diminish the size and cost of 
the marine turbine, while promoting efficiency of both propeller and 
turbine. The Melville-McAlpine gear, designed for this service, is 
essentially a De Laval gear on a large scale. In Power for Nov. 9, 1909, 
will be found a description of the large experimental set of gears built 
for trying out that design. Other trials of the idea have been made, 
but the matter has hardly passed beyond the tentative stage. 

In Engineering, 1911 1, Vol. 91, 463, is described the driving of a 
rolling mill by a 750 h.p. low-pressure Parsons turbine, which acts 
through two pairs of gears, reducing from 2000, through 375, to 70 r.p.m. 
See also Power for May 23, 1911. 

§ 51. Construction of Working Parts. 

(a) The Rotor of the turbine must have a proper form to carry 
the blades and needed strength to resist the forces which come upon it, 
and must be as nearly as possible in centrifugal balance, so that its 
rapid spinning will not cause vibrations. As to form, there are two 






§ 51 (a)] 



CONSTRUCTION OF WORKING PARTS. 



517 



distinct types : the wheel or disc of the impulse turbine and the drum or 
cylinder of the reaction type. In the matter of strength, the major 
stress is generally due to centrifugal force, although resistance to flexure 
by weight may become of first importance in a long horizontal turbine. 
The tangential driving forces, due to dynamic steam action, are rela- 
tively insignificant. 

Of this, as of other working parts, only a few typical examples will 
be given here, with general statement of the principles involved in de- 
sign and construction. For all quantitative considerations of questions 
of design, refer to special works, notably to Stodola's Steam Turbines. 

(b) Disc Wheels. — These are commonly run at higher speeds 
(relative to diameter) than are drum rotors: and 
while the disc, properly proportioned, is far 
stronger than the ring against centrifugal force, 
such extreme speeds as are employed in the De 
Laval turbine tax its capabilities to the utmost. 
The greater strength of the disc is due to radial 
tension, which assists circumferential or ring ten- 
sion. Since the cylindrical area across which 
radial stress acts grows smaller toward the axis, 
a disc of uniform thickness is more severely 
strained at the center than at the rim, and is 
much weakened by a central hole. The sections 
of De Laval wheels in Fig. 358 show how these 
conditions are met: by swelling the disc at the 
middle it is made of approximately uniform 
strength; in the larger sizes the shaft (in parts) is 
fastened to the wheel without going through it; 
while for the small wheel at II the weakening 
effect of the hole is overcome by adding a large 
hub. For the very complex mathematics of cen- 
trifugal stress in a disc, the reader is referred to 
Stodola, or to advanced works on the strength 
of materials; but a few general ideas are set forth in Art. (d). 

At the comparatively moderate speeds in multistage turbines, the 
problem of sustaining centrifugal force is not of extraordinary difficulty. 
In Chapter I, cast-steel wheels are seen in Figs*. 23 and 26, discs of 
pressed plate in Fig. 20. Here Fig. 359 shows the present construction 
of Curtis wheels, with discs of rolled plate, turned thinner toward the 
rim; note the distance ring just outside the row of rivets near the rim, 
which holds the two plates at a definite distance apart. A similar two- 
plate construction is used for the wheels of Curtis marine turbines. 




Fig. 358. — Sections of 
De Laval Discs. 
I, Rotor of larger 
turbines; II, Detail 
of shaft fastening 
in Fig. 18. 



518 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 




Fig. 359. — Detail of Curtis Turbine, showing construction of wheel. From cur- 
rent catalogue, General Electric Company. 

Example 53. — To get some idea of the magnitude of the centrifugal force 
on a high-speed turbine wheel, take the cases of (1) a 4-in. wheel at 30,000 r.p.m. 
and (2) a 30-in. wheel at 11,000 r.p.m., as named on page 24, also (3) of the 
2-meter wheel at 3000 r.p.m. in § 48 (g). If we calculate the centripetal ac- 
celeration V 2 /R or u> 2 R — compare § 31 (b) and (c), Example 35, page 300, and 
Example 41, page 325 — and divide this acceleration by that of gravity, we 
shall have the ratio of centrifugal force to weight force. The three examples 
evaluate as follows: 

Case 1 2 3 

1. Diameter, inches . 4 30 78.8 

2. Diameter R, feet . 0.167 1.25 3.28 

3. Rotary speed N, r.p.m 30,000 11,000 3000 

4. Velocity V, ft. per sec 523 1441 1034 

5. Angular speed <o, rad. per sec 3140 1151 314 

6. Centripetal acceleration a , ft. per sec. 

per sec 1,643,300 1,656,000 324,400 

7. Centrifugal ratio, a + 32.16 .... 51,111 51,500 10,100 

From the last line it appears that the centrifugal force on one cubic inch of 
steel (0.28 lb.), at the mean radii named, is about 14,000 lb. in the De Laval 
turbine. 

(c) Drum Rotors. — In general form, Fig. 356 illustrates what may 
be called the regular type of construction of Parsons rotors; it is made 
up of shaft sections 1 and 2, shell 3, and head 4, all put together with 
shrunk joints: pieces 1, 2, and 3 are of forged steel, piece 4 is a steel 
casting. Of special features in this design, one is the joint lock at J 
(as at the other end also), with interrupted collars which are engaged 
by turning the inner piece through a small angle after it is slipped into 
the heated outer piece. Another is the provision for preventing the 
joint at the high-pressure end from possibly being loosened by excessive 
heating of the shell alone: space K is shut off by disc 5, and steam is 



§ 51 (c)] CONSTRUCTION OF WORKING PARTS. 519 

let in through hole 6; and in order to maintain some circulation, hole 7 
opens into the labyrinth packing of piston Pi near its outer edge. 

The first variation from the arrangement in Fig. 356 is to form 
flanged heads on the shaft sections, and bolt them fast to the shell with 
studs parallel to the axis; this makes the intermediate piece 4 unneces- 
sary. One design (Willans and Robinson) has the shell forged in one 
piece with the shaft section at the high-pressure end. Others use a 
plain shell of the smallest rotor diameter, and make the enlarged sec- 
tions or steps by putting on wheel-like rings, very much as in Fig. 357. 
Marine Parsons turbines, with high and low sections, will have cylin- 
drical drums, or but a small change of diameter. In Fig. 357, the shaft 
and drum sections are steel castings, joined at the middle : in one piece 
with the impulse wheel and projecting equally at both sides there is a 
short sleeve or cylinder, which slips into the open ends of the drum 
sections; the latter are flanged and are held together by bolts, through 
the web of the wheel and parallel to the axis of rotation. A great 
number of illustrations are given by Stodola, in his fourth edition. 

It is highly important that neither rotor nor casing of a reaction 
turbine shall sag, spring, or warp out of shape, whether from weight or 
from irregular heating, because of the close clearance at the vane ends. 
Skillful design, careful annealing of castings for outer casing, and ac- 
curate workmanship are required to obviate trouble in operation. 

(d) Centrifugal Stress. — In § 33 (e), page 326, we have shown 

that the tensile stress in a ring because of centrifugal force is determined 

solely by linear velocity, and that it varies as the square of this V; 

further, that a stress of 20,000 lb. per sq. in. will result from a speed of 

450 ft. per sec. Of course, the ring almost exactly represents the cylin- 

\ drical shell of a drum rotor. Allowing for the added load due to the 

mass of the attached vanes, a speed of about 400 ft. 

jper sec. is considered a good average limit of safe 

'running with ordinary steel. 

To get an approximate idea of conditions in a 
disc, consider Fig. 360. Suppose a narrow sector 
to be cut loose along the lines AO and BO, and 
moved a little way outward in the direction OH; 
then all points along the radial edges OA and 
OB will have the same displacements from their 
original positions, but the movement at C, for Fig. 360. — Diagram 
instance, will bear a much higher ratio to the arc *J ^ s u c strate Stress 
CD than will that at A to the arc AB. Similarly, 

as the disc is stretched by centrifugal force there tends to be a rela- 
tively greater deformation, hence stress, at the middle than at the 




L_ 



520 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

rim. This situation is relieved by radial stretch, which eases up the 
pull on the central metal; but for complete equalization of stress the 
central part must be given the reinforcement of increased thickness. 

(e) Centrifugal Balance. — The problem of bringing the center 
of mass to the rotation axis is first one of getting the most perfect geo- 
metrical symmetry that is attainable with machine-tool appliances, and 
then of trying for and correcting the residual eccentricity by special 
methods. To overcome the effect of the lack of absolute perfection, 
and to avoid the need of very precise and expensive work in balancing, 
De Laval devised his flexible shaft, of which the action depends upon 
the following principles: 

If an eccentric mass is attached to a rotating shaft, and the whole 
mass be thought of as concentrated at its center of gravity, then the 
centrifugal force of this " particle" will act radially outward, tending 
to deflect the shaft in its own direction, and producing a pressure of 
shaft on bearings which constantly changes in absolute direction. 
This type of action has been quite fully discussed under the head of 
shaking force and counterbalance, in § 35. 

But when we consider the mass in its actual distributed state, 
another force action comes into play, which reaches controlling magni- 
tude only at very high speeds. A spinning disc tends to get into the 
simple, stable state of rotation about its own center of mass — this 
tendency being closely analogous to that of the same disc to preserve 
one fixed plane of rotation, or to what is called gyroscope action. 

In the case of any nearly balanced rotating body, as the speed in- 
creases the eccentricity effect at first increases very rapidly, to a maxi- 
mum at what is called the critical speed; then the other tendency 
predominates, and if the shaft is flexible or the bearings a little loose, 
the body will spin quietly on its true axis of symmetry. 

At the speeds usual in large multiple-stage turbines, the degree of 
precision reached with good machine-shop work gives a sufficiently 
accurate balancing for practical freedom from vibration. 

(/) Bearings for Turbines. — In the characteristics of high speed 
but of a generally uniform load to be supported, the turbine is under 
conditions which belong rather to the electric generator than to the 
steam engine, and the design of its bearings follows the lines of the 
former machine. At very high velocity, true alignment and geomet- 
rical perfection of the rubbing surfaces are of the first importance, as 
insuring a uniform distribution of pressure; and with these there must 
be ample lubrication, under some pressure and supplied by an oil-pump 
system. In turbines of any size the bearing shell proper is solidly held 
in the framework of the machine, as indicated in Fig. 357; but there is 



§ 51 (/)] 



CONSTRUCTION OF WORKING PARTS. 



521 



frequently a spherical seating to permit self-alignment with the axis 
direction. The bearing on the inner side of the De Laval wheel — see 
Figs. 18 and 363 I — is free to move sidewise also; but a closer exami- 
nation shows that this is not a bearing at all, in the sense of supporting 
the shaft, but serves rather as a stuffing box. 

The design illustrated in Fig. 361 has several special features. It 
represents the smaller and quicker-running Parsons turbines, where 
some flexibility is secured by placing three thin cylinders between the 
inner and outer shells of the bearing; these are not tightly fitted, and 
the oil films which form between them have a cushioning effect. The 
collar bearing holds the rotor against endwise motion, with the par- 
ticular purpose of preventing side contact and rubbing in the groove 




Fig. 361. — Bearing at Governor End of Westinghouse-Parsons Turbine — at 

right-hand end of Fig. 25. 

or labyrinth packing of the balance pistons. The upper and lower 
halves 4 and 5 are separate, and are adjusted in opposite directions by 
micrometer set screws on the lines S, S. The worm at the right drives 
a cross spindle, which carries a bevel gear for the vertical governor, a 
small eccentric for the admission- valve mechanism (shown in Fig. 378), 
and a crank to drive the oil pump. 

The pivot bearing used at the bottom of large vertical Curtis tur- 
bines is shown in Fig. 362; it differs from the simpler arrangement in 
Fig. 23 chiefly in that the bearing is wholly cut off from possible com- 
munication with the steam space. The face blocks are of hard cast 
iron, disc D keyed to the shaft, C held in the frame, with vertical ad- 
justment by set screws. Oil at high pressure (perhaps 600 to 800 lb. 
per sq. in.) is pumped in at G, filling the recess between the blocks and 
forming a film which keeps the annular contact surfaces from really 



522 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 




0/7 ' Dro/'n 
01/ dupp/y 

Fig. 362. — Pivot Bearing of Curtis Turbine, from catalogue. 

touching. The whole weight of the rotor is thus floated on oil, and the 
frictional resistance is very low. The arrangement in Fig. 23 is intended 
for water instead of oil in the bearing, since it would be almost impossi- 
ble to keep oil out of the exhaust space. 

(g) Stuffing Boxes. — This name, derived from the engine and 
implying close contact and pressure of the packing upon the rod or 
spindle, is applicable to the corresponding part of the turbine as describ- 
ing the function of preventing leakage rather than the manner of per- 
forming that function. Actual contact is used in a few cases; but the 
more generally accepted scheme is based on the idea of avoiding the 
contact of rapidly moving surfaces, while yet allowing but a very nar- 
row (and frequently a very crooked) passage for the flow of steam. A 
number of special devices and methods are used, as will be made clear 
by the examples collected in Fig. 363. 

Plain contact rings are seen at the top of Fig. 23; these rings are 
made of carbon, are held in place by brass skeleton frames, are pressed 
inward by light helical tension springs, and bear upon a brass bushing 
on the spindle. Referring to Fig. 347, which is fairly typical of Curtis- 
turbine conditions, we see that this packing will have to retain a pressure 
of no more than 50 or 60 lb. above atmosp'here; and with the multiple 
effect of a series of rings, leakage can be prevented with only a com- 
paratively small contact pressure. Another example of simple contact 



§ 51 (g)] 



CONSTRUCTION OF WORKING PARTS. 



523 



is given in Fig. 363 I, where air must be "kept out when the turbine is 
running on vacuum. A passage can be opened only by the forcing out 
of the film of oil between journal and bearing, which would require more 
than a pressure of 12 or 13 lb. per sq. in. There will evidently be, how- 
ever, some tendency for the oil to work gradually into the steam space. 

The essential feature of the scheme shown at II and III in Fig. 
363 is the annular space Si, kept filled with steam of nearly atmos- 
pheric pressure by means of a reducing valve from the steam supply 
and a relief valve to the condenser. There will be a gradual flow 
through the very narrow passage permitted by the sleeve at B, outward 
to Si at the high-pressure end, inward from Si at the low-pressure end 
of the turbine — all the " stuffing boxes" being piped to form a com- 
mon system. In effect, the turbine is surrounded by an atmosphere of 
steam at the points where leakage can occur; and then this steam 
atmosphere is shut off from the air by lightly fitting segmental contact 
rings, tied together by helical band springs and pressed inward axially 
by compression springs which exert the force marked F. Oil is sup- 
plied at L. The design at III adds labyrinth packing, both in the 
stuffing boxes and between the wheel chambers — compare Fig. 20. 

A different idea is shown in Fig. 363 IV, which is used to prevent 







«M 


A JH| 


B™!S 


IF 




I. 


feUS 








'\ 






IE 




s 


iKSfe 






Pig. 363. — Packing Devices for Turbines: I, De Laval, from Fig. 18; II, Rateau, 
as in Fig. 20; III, Oerlikon-Rateau, later design; IV, Parsons, from Fig. 25; 
V, Sulzer, Fig. 26; VI, VII, Two Types of Labyrinth Packing. 



524 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

the leakage of air into a steam vacuum. There is, of course, a fairly 
close running fit between the bushing B and the rings C, C ; but the 
passage is closed or sealed by water in the annular space about the collar 
D : this water has a dynamic pressure, acting radially outward, and pro- 
duced by little vanes on the sides of D, which are formed like those on 
the " impeller" of a centrifugal pump. This arrangement has the further 
advantage that by circulating the water the stuffing box is kept cool. 

In V the last two ideas are combined, together with a special form 
of labyrinth packing, made of thin brass plates. These plates or 
washers, only about 0.005 in. thick and separated by narrow rings of 
thicker plate, are bent or flanged where they touch the shaft, as shown 
by the enlarged detail below the main sectional view. 

Labyrinth Packing. — This device, used mostly for preventing inter- 
nal leakage, is made in a wide variety of detailed form, but the idea is 
sufficiently represented by the plain outlines at VI and VII in Fig. 363. 
The first scheme merely provides a narrow, tortuous passage for the 
steam, of nearly uniform cross area; the second and far more effective 
type adds the further retarding influence of large and abrupt changes 
in area of channel. In a long, narrow, straight channel, surface friction 
alone would hinder flow; and the introduction of sharp bends (type at 
VI) gives a much higher resistance. A multist aging of the pressure 
drop (type at VII), with alternate generation of velocity and dissipa- 
tion in eddies, greatly retards the escape of steam through a channel of 
a certain minimum cross area. 

(h) Nozzles and Distributors. — As regards the construction of 
these parts, one typical method is represented by the De Laval nozzle, 

which is made as a separate piece 
and has the form given it by the 
operations of turning, drilling, and 
reaming. It is held in place by 
friction (plus steam pressure) and 
Fig. 364. — De Laval Nozzle, with can be pulled out by means of a 

withdrawing tool that screws over 
the inner end. The shut-off valve is a part of the scheme of power 
control: for light loads, the number of nozzles in service is decreased, 
instead of letting the governor throttle the steam excessively. In larger 
turbines, groups of two to four nozzles are beneath one hand valve. 
Another example of nozzles made separately is seen in Fig. 354; but 
after machining these were bent to curve, and at the mouth were pressed 
to a square cross section. 

High-pressure nozzles for Curtis turbines, with a slight divergence 
as in Fig. 21 or Fig. 320, are cored out in the cast nozzle segments — 




§ 51 (h)] 



CONSTRUCTION OF WORKING PARTS. 



525 









see first two stages in Fig. 23, and compare diagram of admission ranges 
in Fig. 22. These nozzles are round in entrance and throat, but change 
to a squared section toward the mouth; they are smoothed by filing 
and are planed out in the rectangular part by a special machine. The 
low-pressure distributors, profiled as in Fig. 19, are made with pieces 
of ordinary sheet steel, which are set in the cores and cast right into the 
diaphragms: heavy cross struts (like very short wheel arms), above 
these nozzle plates, connect the body of the diaphragm to its rim. 



45 ( 



wdx> i 





^^ 




))))))))))n±)))))))))r>TT> 






4- 



)))))»)))W>)))))))))))))) 

1 ) ))))))) ) )-h-n ))))) ) mim 



_ 



i ))))))))))m>)))))))))Trrrr 



Fig. 365. — Developed Sectional View of Multistage Impulse Turbine, with full 
peripheral admission: outline of the low-pressure part of a Zoelly turbine. 

Figure 365 is intended to illustrate the last point, showing the heavy 
cross struts which, at intervals around the circle and for strength, must 



L^. 




I O I 





I. 





I. 



Fig. 366. — Built-up Nozzles. I, Zoelly design, Fig. 365; II, 
Type of Sulzer, Elektra, etc. 

join the rim and body of the partition disc. The detail of construction 
is shown in Fig. 366 I. Inclined slots are milled (sawed) in the rim of 
the diaphragm wheel and the edge of the cover ring, and the straight 
part of the division plate has projections which go into these slots and 



526 



DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 



are held by light retaining rings. On the cross struts are short tenons 
to resist the steam pressure difference on the diaphragm. The analo- 
gous construction of nozzles for large pressure drop is indicated at II; 
the partition pieces are fastened between cylindrical surfaces in an 
axial-flow turbine, between plane surfaces when the admission is radial. 
(i) Vanes or Blades. — There is a wide variety in the form of 
these essential working parts, and a few typical examples will now be 
given. The De Laval buckets, Fig. 367, are drop-forged from fairly 

hard steel and machined on the contact 
surfaces, their small number permitting this 
rather expensive method. The steam sur- 
faces are left with the forge finish, except 
that the entrance edges are ground sharp. 
A dovetail fastening is used to resist the 
very high centrifugal force on the blade, 
and the form is such that any single bla^e 
can be removed without disturbing the 
others. To minimize the possible damage 
from a bursting wheel, the disc is cut thin 
just inside the rim, with the idea that the 
latter will fly off in small pieces before the whole wheel will burst from 
overspeeding. 

Two other designs using the dovetail fastening, but intended for 
force conditions (due to speed) less severe than those in the De Laval 




Fig. 367. — De Laval Turbine 
Blade. 





Fig. 368. — Zoelly Blading. 



Fig. 369. — Sulzer Blading. 



turbine, are shown in Figs. 368 and 369. Here the blades are made 
from drawn and polished bars of high-nickel steel, and the most impor- 
tant difference between the two schemes is seen in the method of spac- 
ing the blades. Distance blocks, cut from a properly-shaped bar and 
machined with the blades so as to fit the dovetail slot, are used in the 
first case. In the second there is a spacing ring, shown especially at B : 
the roots of the blades are hot-pressed and flattened, as best made evi- 
dent at A, and will then slip into sawed slots in the ring 3. 



§ 51 (i)] 



CONSTRUCTION OF WORKING PARTS. 



527 



The quite common use of vanes formed from rolled plate, by bend- 
ing or pressing, is illustrated in Fig. 370, together with a method of 
attachment to the wheel by rivets and with a band or shroud ring to 
cover the outer ends of the vanes, spacing and steadying them. The 
form of connection shown in Fig. 371 is far stronger and more durable: 




Fig. 370. — Older Rateau Blading, with 
flanged disc. 



Fig. 371. — Present Rateau Blading, 
forked over edge of disc. 



the blade may be either drop-forged as here sketched, or (more usually) 
pressed from sheet metal. 

In some older Curtis turbines, the blades were cut from the solid 
metal of the wheel, as shown at I in Fig. 372. The cutting tool travels 
on a circular path, the tool bar either turning continually or having a 
back-and-forth rotation; in either case, this bar must be drawn back- 





Fig. 372. — Curtis Blading. 

ward in the direction of its axis during the idle part of the movement, so 
that the tool will clear, then advanced for the cutting stroke. This 
method, however, is not very satisfactory, and the blades are now made 
from metal bar of proper shape: two schemes for holding them are 
sketched at II and III. In the first case, the blades are cast into the 
segment of base ring, being held in a core-sand facing which forms one 
side of the mold; they are made of a brass composition soft enough to 
iuse into solid union with the ring. Sketch III shows a simple dove- 
tail fastening, with distance blocks as in Fig. 368, very easy to apply 
when the holding rings are made in a number of short segments, as is 
the usual practice. 



528 



DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X« 



(j) Blading for Reaction Turbines. — The method which has 
been most used for holding the blades of the Parsons turbine is sketched 
in Fig. 373. The blades are cut to length and simply set into the 
grooves, with distance blocks of proper profile between them. These 
blocks have parallel sides (vertically), but are made of a soft metal; 
and after a whole ring has been filled, the blocks are calked, by means 
of a tool which reaches down between the blades, and are thus pressed 
out, more or less perfectly, into the dovetail slot. To give a better grip 
on the blade, a couple of notches are made in the back of it, into which 
the metal of the block will be forced. The blades in the casing are 
held in the same way, except that plain slots are used, not dovetailed. 
The ends of the blades are left free, but the very long blades of the low- 
pressure stages must be braced against a tendency to get into vibration. 
One scheme is to cut a slot in the entrance sides and solder in a wire 
ring, as at A in Fig. 373 : to obviate undesirable effects of expansion this 
ring will be made in several separate segments, instead of being con- 
tinuous all the way around. 

The .scheme shown in Fig. 374, used in this country by the Allis- 
Chalmers Company, has a spacing and holding ring, with slots of 



fel N 



w 
A 





Fig. 373. — The Standard Parsons 
Blading. 



Fig. 374. — Williams-Robinson Blading 
for Parsons Turbines. 



special form into which the ends of the blades fit : these ends are pressed 
into dovetail form, so that the blades are securely held. A narrow 
locking ring presses the main ring into the dovetail; and on the rotor R 
this extra ring is calked into a little side groove. The shroud ring, of 
channel-bar section, holds the blade ends securely, and can be accu- 
rately turned off, so as to make the running fit uniform and as close as 
is permissible, this minimizing leakage. 

(k) Wear on Vanes. — The blading is the weak point in a turbine, 
because it is the part most liable to rapid wear and deterioration. A 
steam jet of very high velocity exerts considerable erosive action, 
greater if the steam is wet than if superheated, and especially aggra- 
vated when particles of solid matter are present, as when boilers prime 






§ 51 (A;)] 



CONSTRUCTION OF WORKING PARTS. 



529 



on dirty water. Breakage of blades is a not infrequent accident in re- 
action turbines, especially at the low-pressure end, where the blades 
are very long. This may result from vibration under steam action, or 
from rubbing at the ends due to distortion of rotor or casing; while if 
water has a chance to collect and be thrown among the vane rows in a 
considerable body, it has enough mass to act as a destructive " foreign 
body," at the speeds existing. 

The materials used for blades or vanes range from various brass or 
bronze compositions, through common low-carbon steel, to a nickel 
steel with so high a proportion of nickel that it will be practically rust- 
less. The Parsons type with its tremendous number of blades calls 
for material that can be easily worked, and with its low steam velocity 
permits a comparatively soft material. The blade bars, of a suitable 
alloy (yellow metal), are generally made by the "extruding" process, 
semifluid metal being forced out through a die and cooled to a solid as 
it issues — after the manner long used in the manufacture of lead pipe. 
The turbines with fewer blades and higher velocities require harder 
materials, but can stand a higher cost per unit part. 

(I) Governing the Turbine. — Three systems of power control 
may be distinguished: the first is plain throttling; the second, admission 




Fig. 375. — De Laval Governor and Vacuum Breaker. 



in puffs; the third, variation of initial nozzle opening. One example of 
each type will now be presented. 



530 



DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 



The governor and admission valve of the De Laval turbine, Figs. 
375 and 376, will serve as the first example: for although this turbine, 
through use of the hand valves described in Art. (h), under Fig. 364, 
may enjoy in a large degree the third type of control just named, its 
automatic regulation is entirely by throttling. An external view of the 
governor appears at H in Fig. 18, which shows how it is carried on the 
end of the power shaft. The centrifugal weights, hollow semicylinders 
in form and marked B, B, in Fig. 375, have knife-edge bearings at 
A, A, in the shell or body E. As the weights swing out, they push the 
block D to the right against the spring, the fixed abutment I for the 
latter being screwed into the outer end of the shell. In normal running 

the spindle G moves the lever L, against 
the light spring at N, and thus raises and 
lowers the double-disc throttle valve shown 
in Fig. 376. Since the valve may not be 
tight even when down on its seat, addi- 
tional security against a runaway is pro- 
vided for in the vacuum breaker. At an 
excessive speed the spindle G can move 
H in the lever L, compressing the spring 
M until D pushes J inward; this opens the 
valve at T, admitting air to the exhaust 
chamber, and thus checking the wheel by 
friction. 

(m) Puff Governing. — The original 
type of Parsons valve gear is shown in 
Figs. 377 and 378, which belong to the 
Westinghouse-Parsons turbine in Fig. 25. 
The valve Vi in Fig. 377 is not held fast 
by the governor at the particular height 
which will make the opening just large 
enough, but is given a continuous oscillating movement, so as to 
admit the steam in puffs. The governor mechanism, outlined in Fig. 
378, moves the little pilot valve F, which opens and closes the exhaust 
port E. When E is closed, steam coming through A lifts the piston 
C, opening the valve; when E is open the steam escapes from the cyl- 
inder more rapidly than it can get past the adjusting valve B, and the 
spring H pushes the valve down. Piston G has a dashpot action, 
while lever K is for opening the valve by hand, so as to prevent stick- 
ing fast when the turbine is standing idle. Under light load the valve 
Vi is shut during the greater part of the oscillation period; with heavy 
load the oscillation may entirely disappear because valve F will not 




Fig. 376. — De Laval Governor 
Valve. 



§ 51 (to)] 



CONSTRUCTION OF WORKING PARTS. 



531 



open port E at all. The steam passing through this controlling system 
need not be wasted, but can be returned to the turbine at a lower- 
pressure point. The bypass valve for overload, V 2 in Fig. 25, is actu- 




Fig. 377. — Parsons Admission Valve and Controlling Mechanism: this is valve Vi 

in Fig. 25. 

ated by steam in the same manner, but its pilot valve is given only a 
simple displacement, without oscillation. 

The governor mechanism is sketched in Fig. 378. The eccentric E 
is on the same spindle with the wheel driven by the worm shown in 
Fig. 361, and the lever 1 is oscillated once to every so many revolutions, 



532 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

say 5 or 6, of the rotor. The governor being at one end of the machine, 
piece 3 takes the form of a long rod or shaft, with arms keyed to it. The 
function of the governor is simply to raise and lower the fulcrum A. 

In this system of control, the turbine has a periodic pulsation of ad- 
mission pressure. Steam-channel areas and vane angles have been so 
designed, presumably, as to give best performance with steam of full 
pressure. Most of the steam used enters during the high-pressure por- 
tion of the cycle period, hence works to better effect than if at the 




Fig. 378. — Outline of Governor and Valve Gear, Westinghouse-Parsons Turbine. 

equivalent mean steady pressure. Against this argument must be set 
the fact that a part of the steam works at very low efficiency; while the 
alternate acceleration and retardation of the whole steam current cer- 
tainly seems likely to exert a harmful influence. No data are available 
as to the manner in which the pulsations extend through the turbine to 
the low stages, but there will evidently be a tendency to damp them 
out. In a many-stage impulse turbine, with its large enclosed steam 
spaces in the wheel chambers, such modulating action would be very 
strong — but the scheme is never used with that type of machine. 

As between the two systems of puff admission and steady throttling, 
no comparative data are extant : the difference in net results is probably 
so small that repeated and very careful tests of the same machine 
would be needed to establish its existence and amount. One un- 
doubted merit of the Parsons device is, that since the valve is in con- 
tinual motion it is never likely to stick fast and perhaps cause the 
governor to lose control. Most builders of Parsons turbines have used 






§ 51 (m)] 



CONSTRUCTION OF WORKING PARTS. 



533 



this valve action, with variations in mechanical detail of the driving 
apparatus, but some have gone to plain throttling. Concerning mixed- 
type design, it is enough to cite the facts that the Westinghouse Machine 
Company have carried puff governing into their double-flow turbine, 
while the Sulzer turbine (of which Fig. 26 is an early example) is governed 
by throttling. 

(n) Cut-off Control. — The scheme of automatically regulating 
the number of first-stage nozzles open for admission was first worked 
out and applied in the Curtis turbine. The inlet valves, generally 
about eight in number and each controlling a small group of nozzles, 
stand in a row in a steam box or 
chamber, S in Fig. 379; this valve box 
subtends but a small arc of the tur- 
bine circumference, and in the larger 
machines is one of a pair. At I is 
shown a cam mechanism for lifting 
the valves, at II a steam-actuated 
valve. The governor works, of course, 
on the relay principle : acting through 
a self-centering gear essentially equiv- 
alent to that shown in Fig. 290, it 
moves the slide valve of an oil-oper- 
ated " hydraulic " cylinder. From the 
crosshead of the latter comes the rod 
H, which turns the cam shaft B ; and 
the cams along this shaft, one to a 
valve, are set in series, each a little later than the preceding one, or a 
certain number of degrees behind it. Under any particular load there 
will be a number of valves wide open, one partly open, the rest closed; 
the single valve that is just in the act of opening for any position of 
the cam shaft gives the close gradation of power. 

With steam-actuated valves, as at II, the governor operates a series 
of small pilot valves, one of which determines whether steam of full 
pressure shall be admitted above the piston P or whether this space 
shall be opened to exhaust. In the latter case the valve will be lifted, 
because the piston is larger in diameter than the valve disc. The pilot 
valves are generally moved by a cam shaft like that here used for the 
main valves; while magnet lifts have also been employed. 

The governor, shown in Fig. 380, is carried on the top of the main 
spindle, above the generator. The weights A, arranged very much as 
in Fig. 375 and similarly pivoted on knife edges, pull at B on the ten- 
sion spring D. Rod C, which turns, of course, with the rest of the 




Fig. 379. — Nozzle Valves for the 
Curtis Turbine. 



534 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 




Fig. 380. — Governor of the Curtis Turbine. 



governor, is connected by a ball-bearing joint at 
E to the stationary lever, the outer end of which 
moves the pilot valve of the oil cylinder. At F is 
an auxiliary spring for changing the running speed, 
which may be adjusted from the switchboard by a 
little motor G. 



Z3n3> 





Fig. 381. — Self-acting Nozzle Valve 
for De Laval Turbine. 



Self-acting Valves.— In Figs. 381 and 382 are FlQ 382 . —Automatic 
given two examples of valves operated by pressure Bypass Valve for 

differences which arise within the turbine. The r urti f ? urbi S?' o 1 ^" 

larged from Pig. 23. 

first is an automatic substitute for the hand valve 

shown in Fig. 364. With full pressure in the valve chamber, the grooved 

plunger is pushed to the left against the spring; but when the governor 



§ 51 (n)] CONSTRUCTION OF WORKING PARTS. 535 

throttles the steam, the spring force predominates and closes the valve. 
For the position and connections of the inter-stage valve in Fig. 382, refer 
to Fig. 23. It serves the special group of second-stage nozzles marked 
Nb in Fig. 22, opening when, because of heavy load and a large initial 
admission, more steam gets in than can be accommodated by the regu- 
lar second-stage nozzles. With pressure from the first wheel chamber 
on top and that from the second chamber below, the valve opens when 
the difference between these exceeds the push of the spring. 

(o) Effect of Governor Action. — The question, What is the 
effect of a change from normal load, and how does it differ in the two 
cases of throttling and of cut-off control? will now be briefly con- 
sidered. As characteristic of normal-load running, we assume that in 
all the stages the steam velocity bears the same ratio to the vane speed, 
according to § 46 (j), and that the final drop to exhaust pressure just 
gives to the last stage its proper share of energy. The chief determi- 
nant of this action is the manner of variation of the channel section, as 
pointed out in § 49, and at each point along the channel there will be a 
characteristic normal pressure, with which the local pressure under 
changed conditions may be compared. 

The most obvious result of a decrease in the amount of steam ad- 
mitted is to lower the local pressure all along the line, while an increase 
will raise it. This will give the last stages a smaller proportion of the 
total energy development at light load, a larger share at heavy load. 
Under very light load the exhaust pressure tends to creep up into the 
turbine, the gradient through the last stages being only enough to 
maintain the flow; under heavy load, high pressure backs up toward 
the entrance. 

Now plain throttling, which cuts down the steam pressure at en- 
trance, tends to keep the division of work among the stages more nearly 
equal at light loads — while diminishing, of course, the total energy 
available. The cut-off method admits steam at full pressure, but it 
has a big drop through the initial stage, and thereafter the local pressure 
will be about the same as with the first manner of control. The advan- 
tage of the second method depends upon the ability of the first stage to 
absorb effectively the relatively large energy made available for it; but 
since such a capability will always exist to some degree, it seems that 
the scheme of having all the pressure drop within the turbine itself is 
inherently better than that of allowing a considerable part of the drop 
to take place in the governor valve. 

Control of successive nozzle areas, most practicable in few-stage 
several-impulse turbines, has not been carried in the Curtis turbine 
beyond the use of the bypass valve in Fig. 382 : it is held that the possi- 



536 DESIGN AND CONSTRUCTION OF THE TURBINE. [Chap. X. 

ble small gain will not overbalance the disadvantage of greater mechani- 
cal complexity. Of the Schulz turbine represented by Fig. 348, quite 
extensive tests are described in the reference from No. 34 in Table 20: 
naturally, better economy resulted from an equable division of work 
among the stages than from an irregular distribution. Puff admission 
has somewhat the effect of cut-off control, in that most of the steam 
enters at higher pressure, as just pointed out in Art. (m). With the 
resulting fluctuation of driving force, the fly-wheel effect of the heavy 
rotor is required for the maintenance of steady speed. 









CHAPTER XI 
SUNDRY STEAM APPLIANCES 

§ 52. Steam Jet Apparatus 

(a) Action of Entrainment. — The steam jet from a nozzle, be- 
side being applied to the driving of turbine vanes, may be made to 
impel a stream of air or water. The steam discharges into a space 
filled or supplied with the substance to be moved; there it picks up or 
entrains a certain amount of this substance, forming a mixed jet of 
greater weight but much smaller velocity; and then this resultant jet 
is discharged through a suitable retarding nozzle against a pressure 
higher than that at the mixing point. 

These devices are, mechanically, the simplest used for applying the ex- 
pansive energy of steam to work performance, since they have no mov- 
ing machine parts. They are, however, of very low efficiency: large 
wastes of kinetic energy occur in the mixing operation, and in the re- 
tardation of the current against rising pressure there are further losses 
of effect. Besides, to insure delivery, the discharged jet must have a 
very considerable excess of velocity and energy, which is necessarily 
dissipated into heat as it comes to rest. 

(b) Steam Blowers, used for producing draft for boiler furnaces, 
are of two types. The first is the exhaust jet of the locomotive, in 
which the whole body of steam used by the engine mixes with the 
products of combustion, drawing them into an enlarged jet which is 
expelled up the smoke stack. These gases, coming from the boiler 
tubes into the smoke box, are at a temperature much above that of the 
exhaust steam: consequently the steam is not condensed, but is rather 
dried and superheated, and we have the case of two gases mixing. A 
typical example is outlined in Fig. 383, a good deal of nonessential 
detail being omitted in the drawing, especially the spark-arresting 
screens; these serve also to break the force of the current from the 
tubes into the space above the exhaust nozzle N, and to deflect the 
greater part of it downward, so that the jet draws mostly from below. 
This is from a large locomotive, where the stack has to be let down 

537 



538 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 



into the smoke box, and a dead space is left above the horizontal 
partition P. 

The second type of blower is illustrated by the example in Fig. 384, 
where a small jet of high-pressure steam is used for moving a stream of 
air relatively much larger than that in the locomotive (as compared 
with the weight of the steam), but against a much smaller resistance. 
Further, air of ordinary temperature is drawn into this blower, so 
that the steam will be partly condensed in the formation of the 




Y///////////A 

Fig. 383. — Locomotive Smoke Box. 




Fig. 384. — Forced-draft Blower. 



mixed jet — the action approaching that of the injector in this re- 
spect. Note how the entering air is split up into several concentric 
divisions, with the intention of reducing the eddy loss during the mixing 
operation. 

The following example, worked out with assumed data, will show 
the method of computing the efficiency of this sort of apparatus in 
actual operation, and will give some idea of its probable value for the 
first type: 

Example 54. — In a locomotive boiler, 1 lb. of coal will evaporate about 
6 lb. of water, and the gaseous products from 1 lb. of coal will weigh about 18 
lb., so that there will be 3 lb. of gas to 1 lb. of exhaust steam. We assume that 



J 



§ 52 (&)] 



STEAM JET APPARATUS. 



539 



the mixture of hot gas and superheated steam will have a temperature of 400 
deg. fahr., and that the gas alone has the same density as pure air. For air at 
400 deg., disregarding the small variation from atmospheric pressure in the 
smoke box, the specific volume would be, by Eq. (12), 

v = 12.4 X f^ = 21.7 cu. ft. 
492 

At the same pressure and temperature, the pound of steam measures 34.7 cu. ft., 
by Table VI: then the whole volume discharged through the stack, per pound 
of steam, is 34.7 + (3 X 21.7) = 99.8, or say 100 cu. ft. 

The static resistance overcome is the pressure difference, or the "vacuum" 
in the smoke box, which may be assumed as equivalent to 4 in. of water column. 
One foot of water column equals 62.4 lb. per sq. ft., so that the resistance is 
20.8 lb. per sq. ft.; and the work done in expulsion will be 100 X 20.8 = 2080 
ft. lb. 

Now the steam is expelled from the cylinder and forced through the nozzle 
by the back pressure upon the piston, over and above the atmosphere, together 
with the available work of the uncompleted expansion, represented by the tri- 
angle CHD in Fig. 57; this may easily amount to 4 lb. per sq. in. through the 
whole steam volume; and taking the latter to be 24 cu. ft., with allowance for 
the condensation due to work done in the cylinder, we get about 

/ 4 X 144 X 24 = 13,820 ft. lb. 

as the energy of the steam jet per pound of steam. Then the mechanical 
efficiency of the apparatus is 

= 0.151. 



E = 



13,820 



Referring forward to Eq. (244), which applies equally well to this case, we 
find the limit of efficiency in the entraining operation, with our ratio of masses, 
to be about 25 per cent, the other 75 per cent of the jet energy being necessarily 
changed into heat: and comparison of the realized 0.15 with the maximum at- 
tainable 0.25 gives an efficiency of 0.15 -s- 0.25 = 0.60 for the operation of jet 
retardation and pressure- work performance. 




Fig. 385. — The Simple Injector. 

(c) The Injector. — The simplest type of this apparatus is out- 
lined in Fig. 385, where all structural detail is left out, and only essential 
form is shown. Steam from the boiler enters at S, and its admission to 



540 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 



the nozzle is controlled by the hand-regulated valve V. To start the 
injector, this valve is opened a little way, and the steam jet at first 
draws out air from the water chamber W and from the water pipe, 
until the vacuum is sufficient to lift the water; as soon as the flow of 
water is established, steam is turned on full, and the mixed jet, formed 
by condensation of the steam in the tube T, all reduced to water by 
the time it gets to the throat C, and then slowed up in the retarder R, de- 
velops enough pressure to open the check valve K and force itself into 
the boiler. The overflow F permits the escape of the mixed steam and 
air at the start, and of the first water, which is propelled by a jet of 
steam too weak for the regular discharge. This overflow is located at 
a part of the tube where the pressure in the jet is less than that of the 
atmosphere, in normal running; and the automatic check valve at F 
prevents air from getting in to spoil the vacuum. 

The rate of delivery of an injector can be varied over a considerable 
range — in some cases from full capacity to as little as 40 per cent of 
that rate. In the simple form, this regulation is made chiefly by chok- 
ing down the current of water in the suction pipe; something can be 
done by diminishing the supply of steam, but if this is cut down very 
much, the jet may become too weak for expulsion, and the injector 
will " kick back." 

(d) The Compound Injector. — The injector with only one tube 
is not very sure in its action if the supply water must be lifted through 




Fig. 386. — The Double-tube Injector. 



any considerable height: to overcome this difficulty, two working jets 
are used, one for suction, the other for forcing. The general arrange- 
ment and the form and dimensions of the working parts of the in- 
jector outlined in Fig. 386 are copied from an actual design, the " Met- 
ropolitan": but besides the omission of details of construction and the 



§ 52 (d)] STEAM JET APPARATUS. 541 

mere indication of such parts as stuffing boxes, some of the essential 
parts are transposed from their regular positions, so as to make a clearer 
illustrative drawing. 

The stems of the two valves Vi and V 3 are rigidly connected by 
external side bars, so that they must move together, and are controlled 
by a suitable lever handle at the left. When the injector is idle these 
are pushed over to the right so that both steam valves, Vi and V 2 , will 
be closed and the overflow V 3 wide open. To start, the handle is 
drawn back just a little, bringing the lifting valve Vi into the position 
shown at A, and admitting a small amount of steam through the 
chamber S 2 to the lifting nozzle Ni, so as to establish the suction. The 
piston P keeps the nozzle N 2 shut off, not only during this preliminary 
admission of steam, but also until V 2 has been given quite a movement. 
In fact, Vi is not essential to the working of the apparatus, but is rather 
designed to equalize the pressure on the two sides of V 2 before this 
larger valve is moved, so that there will be no great resistance offered 
to the moving of the handle. In order to insure prompt filling of the 
whole injector with water at the start, the overflow is put on the dis- 
charge chamber W 3 ; and the passage through the forcing tube T 2 is 
supplemented by the check valve V4. 

As soon as a good stream of water appears at the overflow, the 
handle is pulled all the way back, giving full admission past the main 
valve V 2 to the steam chamber, and closing the overflow: in the draw- 
ing, the injector is not quite wide open, and there would be some waste 
of water through the overflow valve. The small valve V 5 , at the lifting 
nozzle, is not intended ever to be closed, but is adjusted by hand so as 
to regulate the rate of delivery by varying the amount of water sup- 
plied to the forcing tube T 2 . 

(e) Theory of the Injector. — In all these devices for impelling 
fluids by means of a jet of steam, there are two principal ways in which 
the available kinetic energy of the jet is wasted or dissipated: namely, 
in the operation of mixing or entrainment and in that of retardation. 
The first loss is necessarily very large, and its amount may be approxi- 
mately reasoned out as follows : 

If a small body moving at high speed impinges upon a larger body 
moving slowly, but in the same direction, the sum of the momenta, or 
of the several mass X velocity products, will be the same before, during, 
and after the impact. If the bodies are nonelastic, they will move to- 
gether after impact, and there will have been a loss of kinetic energy : for if 

M l V 1 + M2V2 = (Mi + M 2 ) V, .... (242) 
then will Mi7i> + M ^ Vi (Mi + Ma) y 2f 



542 SUNDRY STEAM APPLIANCES. [Chap. XI. 

or the sum of the original kinetic energies be greater than the energy 
of the combined mass.* Let E be the latter quantity, and change it 
from (Mi + Mi) V 2 to 

' (M 1 V 1 + M 2 v 2 y 
M l + M 2 

by Eq. (242). Now subtract this from the original energy 

E 1 = M 1 V 1 2 -\-M 2 V 2 2 : 

after reduction, the difference, or the decrease of kinetic energy, is 

With elastic solid bodies, there is rebound after impact, in which 
most of the energy that has been absorbed in compressing the solids is 
restored; with fluids, mingling together, any such action is impossible, 
and Eq. (243) therefore applies to the operation under consideration. 
Let Mi stand for the steam and M 2 for the substance to be moved, 
which might be called the load; usually the initial velocity and energy 
of the latter are relatively small, and by dropping V 2 from Eq. (243) we 
get for energy lost the simple approximate expression, 

In the injector, a good working proportion is 10 or 12 lb. of water to 
one pound of steam; then the wasted energy will be TT to T § and the 
effective energy only -^ T to y 1 ^ of that in the steam jet. The latter may 
have a velocity of 2400 to 3000 ft. per sec. and a kinetic energy of 
90,000 to 140,000 ft. lb. per pound of steam (see Table 6), varying with 
both the initial pressure and that at the mouth of the steam nozzle. 
Disregarding V 2 in Eq. (242) and using yV as an average value for the 
efficiency in mixing, or for Mi/ (Mi + M 2 ), we have V = Vi -s- 12 =200 
to 250 ft. per sec. ; and with this V the 12 lb. of mixed jet, or (Mi + M 2 ), 
will have the energy E = Ei -^ 12 = 7500 to 11,700 ft. lb. All the 
rest of Ei is changed back to heat during the mixing of the fluids. 

It is not possible to calculate the efficiency of, or the energy waste 
in, the operation or retardation and the performance of pressure work; 
but it is certain that the energy of the jet and its velocity (E and V as 
just found) must be considerably greater than the work of expulsion 

* Omission of the factor \ from the expression for kinetic energy, a mere matter 
of present convenience, does not effect the relation deduced and applied. 



§ 52 (e)] STEAM JET APPARATUS. 543 

against, and the velocity of efflux due to, the final pressure. The last 
is found most conveniently by the hydraulic equation 



V = V2gh (245) 

To get the effective head h, divide the net discharge pressure by 
(61.5 -i- 144) = 0.427: here 61.5 is used instead of 62.4 as the weight 
of one cubic foot of water in order to take account of the high tempera- 
ture of discharge from the injector. 

Suppose, for example, that the injector feeds a boiler against a gage 
pressure of 150 lb., and that the water is lifted 10 ft. : then 150 -5- 0.427 = 
351 ft.; adding the 10 ft. of suction head and substituting in Eq. (245) 
we set 

V = V64.3 X 361 = 152.5 ft. per sec. 

If the mixed-jet velocity were V = 225, as above, the efficiency in re- 
tardation and expulsion would be 

'V'\ 2 /I ^9 *>\ 2 

1 =0.46. 



V ) \ 225 

(/) Test of Injector Performance. — In making a test of the 
working of an injector, it is enough to measure the water drawn in and 
to observe the temperature and pressure of suction and of discharge, 
beside getting the pressure and quality of the steam supplied. The 
amount of steam used can be found by means of a thermal equation, in 
which the small quantity of heat converted into work may be disregarded. 
In the operation of mixing, the heat given off by 1 lb. of steam, above 
the discharge temperature t 2 , is taken up by w lb. of water in being 
raised from the suction temperature to to this same U. Having gotten 
from the steam table the total heat h\ of the entering steam, the equa- 
tion is 

/*!- fe-32) =w(t 2 -to) (246) 

An example will illustrate the relations involved and the method of 
getting results. 

Example 55. — An injector supplied with steam at 94.5 lb. by gage, with 
2.6 per cent of moisture, draws water at the rate of 3240 lb. per hour, showing 
the temperatures t = 72.6 deg., t 2 = 156.3 deg.: the supply of water is at 16 ft. 
below the injector, and the discharge pressure is 99.2 lb. by gage. How much 
steam is used per hour, how much work of pumping is done per pound of steam, 
and what is the thermodynamic efficiency of the injector as an engine? 

For this steam, at 109.2 lb. abs., 

h x = 1188.1 -0.026 X 883.1 

= 1188.1 - 23.0 = 1165.1 B.t.u. 



544 SUNDRY STEAM APPLIANCES. [Chap. XL 

Then by Eq. (246) the water pumped per pound of steam is 

1165.1-124.3 1040.8 10yf0 « 
W = 156.3 - 72.6 = W " 12 ' 43 lk 

Dividing the total water weight of 3240 lb. by this ratio, we find the steam per 
hour to be 3240 ^ 12.43 = 261 lb. 

The pumping work to be credited to the injector, per pound of steam used, 
is the forcing of 13.4 lb. of total discharge, at 61.0 lb. to the cubic foot against 
a. net pressure of 99.2 + (16 -t 2.31) = 106.1 lb. per sq. in. Solving by the 
pressure-volume method of Eq. (23), we have 

U = 144 X 106.1 X Jfi = !5,280 X 0.220 
ol.O 

= 3360 ft. lb. or4.32B.t.u. 

Now out of a total heat supply of 1165.1 - 124.3 = 1040.8 B.t.u. (estimated 
above the temperature of the water discharged), only 4.32 B.t.u. is effectively 
transformed into work; and the thermodynamic efficiency has the low value 

E = ££=■ = 0.00415, or 0.42 per cent. 
1041 

(g) Range of the Injector. — In the matter of discharge pressure, 
it is possible, by suitably proportioning the steam nozzle and the inlet 
to the mixing tube, to have this pressure far above that of the steam, 
even using the exhaust from a noncondensing engine to feed the boiler. 
In this case the water pumped per pound of steam will be relatively 
small, because the energy of the steam jet is small; consequently the 
supply water must be cold, so that the steam will be condensed without 
making the final temperature too high. Further, the fact that this 
temperature must be high precludes the lifting of the water by suction, 
because the attainable vacuum in the injector will be small. 

Ordinary high-pressure injectors are usually proportioned so as to 
deliver against a pressure from 20 to 40 per cent above that of the 
steam — that is, in regular working there is a large excess of energy in 
the water jet over just what is necessary for delivery. 

It is frequently desirable to use feed water of fairly high initial 
temperature, as from the hot well of a condensing plant. The upper 
limit of suction temperature in a well-proportioned injector will be 
about 130 deg. fahr. — which in Example 55 would make t 2 about 212 
deg. — so that feed at from 90 to 110 deg. is entirely practicable; but 
of course this water must be supplied to the injector, if of the simple 
type, at or above its level. 



§ 53 (a)] CONDENSERS AND AIR PUMPS. 545 



§ 53. Condensers and Air Pumps 

(a) Principle of Condensation. — Suppose that a closed vessel 
has been filled with pure (that is, air-free) water, and that this water 
has been partly withdrawn; then the space above it will be filled with 
vapor, of which the " tension " or pressure will be just that correspond- 
ing to the temperature existing, according to the relation given in the 
steam tables. At 120 deg., for instance, the absolute pressure would 
be 1.69 lb., at 100 deg. 0.95 lb., at 80 deg. 0.51 lb., and so on. The 
condenser is always a closed space containing water and vapor, but con- 
ditions are complicated by the unavoidable presence of a small amount 
of air; this has entered the boiler in the feed water, has leaked into the 
engine or turbine or exhaust pipe, or has come in with the cooling 
water. To maintain a certain vacuum (or low absolute pressure), two 
things are necessary: there must be an ample supply of cooling water, 
so that the heat of the steam can be taken up with but a moderate rise 
of temperature in this water, and the products of condensation must 
continually be removed. The water of condensation is very easily 
taken out; but to get rid of the air is a more troublesome problem, as 
is indicated by the fact that although this air is but a minute fraction 
(by weight) of the substance handled by the vacuum pump, the latter 
is commonly called an air pump. 

(b) Types of Condensers. — The primary division is into the two 
main classes of jet or mixing and of surface condensers, typically rep- 
resented by Figs. 387 and 389. In the first, water enters at B and is 
spread out in a conical spray by the distributor D, which serves also as 
a regulating valve; steam enters at A, and after condensation in the 
space just below D the combined stream sweeps down through the 
neck F into the air pump, and is finally discharged at J. The water 
current must fill the narrowest part of the channel, below F, and its 
velocity must be greater than the speed with which bubbles of air can 
rise through water, so that the air will be effectively carried out, and 
not allowed to accumulate. The surface condenser, Fig. 389, is a box 
or tank nearly filled with a closely-spaced body of small brass tubes 
(f in. to 1 in. diameter, outside), through which water flows. To the 
vacuum pump goes only the condensed steam and the air that came 
with it, while a separate circulating pump drives the cooling water 
through the tubes. A jet condenser, if placed not more than 15 to 20 
ft. above the supply, will draw its own cooling water by suction; but 
water under pressure must be available for starting or " priming " the 
condenser. 



546 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 



> 'E 



RELIEF Valve 





Water 



From t 

ENGINEm 




M 



From 
Pump 




Fig. 387. — Simple Jet Condenser. 



Fig. 388. — Barometric Condenser. 



(c) Removal of Condensate. — The jet condenser can be evacu- 
ated without the use of a vacuum pump: one scheme is illustrated in 
Fig. 388, the other, the ejector condenser, can be described in a few 
words. The barometric condenser is raised so high above the level of 
the hot well that the top of the column of water in the tail pipe, if de- 
termined by the static lift of the vacuum, will be a few feet below the 
condenser proper — or the latter will be about 35 ft. or more above 
overflow level in the tank into which the tail pipe discharges. Then 
the current of warm water flows out by gravity and, with the help of a 
narrow-necked ejector to insure entrainment, carries the air with it. 



§ 53 (c)] 



CONDENSERS AND AIR PUMPS. 



547 



A pump is needed for raising the cooling water, but is helped by the 
suction lift of the vacuum. 

The ejector condenser works on the principle of the injector, the 
discharging current being given a high enough velocity to carry it out 




Vacuum Pump Circulating Pump 

Fig. 389. — Typical Simple Surface Condenser. 

against the pressure of the atmosphere. Water enters at the top 
through a central nozzle, and steam is admitted to and guided against 
the water stream by a series of narrow conical passages in and around 
the wall of the mixing tube: in effect, a series of thin annular steam jets 
impinge upon the stream, and impart some of their velocity to the 
combined current. Water should flow to this con- 
denser from a supply at or above its own level. 

The difficulty of air removal is greatly aggravated 
by increase of vacuum beyond a certain point, or by 
lowering condenser pressure to what is desired in 
steam-turbine practice. Especially, entrainment by 
the main water current, as in Figs. 387 and 388, be- 
comes less effective and complete as air density FlG - . 3 ?°-~ Tu . be 

._ . , . ., Joint for Surface 

decreases and specific volume grows; and similar Condenser. 

troubles arise in the method of combined withdrawal 
from a surface condenser, represented by Fig. 389. To facilitate the 
handling of large volumes of air and vapor mixture, the two products 
of condensation are usually separated in a high-vacuum plant. Most 
simply, water collects alone in a supplementary tank or " hot well " at 
the bottom of the condenser, as indicated in Fig. 396, whence it is with- 
drawn by a small pump, of either piston or centrifugal type : this pump 
may be controlled by a float in the hot well, so as to maintain there a 
constant water level. A separate " dry-vacuum " pump, built very 
much on the lines of an ordinary air compressor, now takes care of 
the air from the condenser. A similar separation of function with a 




548 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 



jet condenser is shown in Fig. 393: there is some entrainment of air 
by the current in the tail pipe, but this is supplemented by a dry-air 
pump. 



30 40 50 60 DEG. 80 Fahr. 100 120 

Fig. 391. — Volume of Air and Vapor Mixtures. 



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140 



The " air " in and from the products of condensation is not really 
pure, dry air, but is a mixture of the latter with uncondensed water 






§ 53 (c)] CONDENSERS AND AIR PUMPS. 549 

vapor. The nearer pressure and temperature come to being in the 
steam-table relation (or in that of boiling point to pressure), the larger 
is the ratio of vapor to air in the mixture filling the open spaces of the 
condenser, not occupied by liquid. As the air mixture is cooled below 
the steam-saturation temperature for the pressure existing, or as the 
pressure in the condenser rises above that corresponding with the tem- 
perature existing, the volume to be handled by the air pump dimin- 
ishes rapidly. 

(d) The Law of Gaseous Mixtures. — In general, if air and 
water are confined in a vessel, equilibrium of composition exists in the 
space above the water only when the air is " saturated " with vapor. 
This means that as much vapor will have been formed from the water, 
and diffused through the air, as is needed to bring the combination to 
the proportion fixed by the law of gaseous mixtures, with vapor tension 
as the determinant. In simplest statement, this law is that the product 
pv for the mixture is the sum of the pv's of the components.* With 
two gases, it is most obvious to think of them as measured, at pressure 
p, by the products pv± and pv 2 , where v\ + v 2 = v. But after diffusion 
each is spread out through the whole volume v, so that the measures 
change to piv and p 2 v, with pi -\- p 2 = p. In other words, each part of 
the mixture exerts a part of the total pressure which is proportional to 
its relative quantity (by volume, not by weight). 

Now let one component be a vapor in presence of its liquid and hav- 
ing a certain specific pressure at the temperature existing: then the 
mixture (or the gas) will be saturated when the vapor is to the whole as 
its tension is to the whole pressure. If there be more vapor, as in the 
exhaust coming to the condenser, it will turn to liquid (without change 
of pressure or temperature) when the way is opened for escape of latent 
heat; if there be less vapor, as in the ordinary atmosphere, evaporation 
tends to take place. Since the mixture in the condenser is always 
arrived at from the side of excess of vapor, it is sure to be saturated. 

Another concept, which underlies hygrometry or the measurement 
of atmospheric humidity, is that air is saturated when the least cooling 
(which involves decrease of vapor tension) will initiate the formation of 
mist, or result in the deposit of dew. 

(e) Volume of Air and Vapor Mixtures. — This matter is put 
into quantitative shape in Fig. 391, which covers the range of con- 
denser conditions. Each curve is drawn for a particular pressure, from 
0.3 to 3.0 lb. absolute as marked, and that for 1.0 lb. is lettered, to 
help the explanation. The basal quantity of air alone is that which 

* This is for a physical mixture, distinct from a chemical compound or a solu- 
tion, as of gas in liquid. 



550 



SUNDRY STEAM APPLIANCES. 



[Chap. XL 



measures 1 cu. ft. at 14.7 lb. abs. and at 60 deg. fahr. Substituting in 
Eq. (12), making it pv = w X 0.37 T, we find the weight of this cubic 
foot of " free air " to be 

14.7 X 1 



w = 



0.0764 lb. 



0.37 X 520 

Then its volume, with varying temperature at a particular pressure, is 

0.37 (t + 460) 



v a = 0.0764 



0.02827, , 13.00 /0 _ 

•t-\ -. . (247) 



p V V 

kip = 1 lb., line AB shows the value of this v a , and its slight variation 
with temperature. The right-end limit B is at the temperature of 
steam saturation for the governing pressure, which is the highest tem- 
perature attainable by the air and vapor mixture under that pressure. 

I.Or 



0.9 

0.8 

01 

0.6 

0.5 
Air 
0.4 

BY 

0.3 
VOL. 

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30 40 



50 60 Deg. 80 Fahr. 100 120 

Fig. 392. — Proportions of Air and Vapor Mixtures. 



140 



The ordinate distance between line AB and curve DEF represents 
the volume of vapor that accompanies the air beneath AB, according 
to the concept that both components are raised to and measured at the 
full pressure p. At the upper limit BC this distance is infinite, since 
the pressure-temperature relation of the steam tables is rigorously true 
only for perfectly pure vapor. Curve FED therefore has the line CB 



§ 53 (e)] CONDENSERS AND AIR PUMPS. 551 

as an asymptote; but its very rapid fall to the left of CB shows how 
greatly the volume of mixture (from the base line to the curve) is dimin- 
ished by cooling below the temperature of steam saturation. 

The ordinate of curve DEF is found by the method of pressure ra- 
tios, as set forth in the last article. Let p be the pressure in the con- 
denser and p s the characteristic steam pressure or vapor tension, at an 
observed or existing temperature t, lower than that which corresponds 
with p for steam. Then the whole volume v is to the air volume v a 
as the whole pressure p is to the partial air pressure (p — p a ), or, 

v=— ^— v a (248) 

P-Ps 

Another method, based more directly upon the physical state of the 
air as diffused through the whole space v and exerting the partial pres- 
sure (p — p a ), is to substitute the latter pressure in Eq. (12), with the 
actual temperature, whether for one pound of air or for some other 
quantity; the resulting air volume will also be the volume of the mixture. 
The proportion of the mixture or its ratio of composition is shown 
in Fig. 392, as a variable with temperature and for the same set of con- 
stant pressures that was used in Fig. 391. With the whole height rep- 
resenting unity, the ordinate below a curve, or the fraction of air, is 
v^/v or (p — p s )/p; while that from the curve to the top line, show- 
ing fraction of steam, is vjv or pjp. 

Example 56. — Determine numerical values with p = 1.2 lb. for Figs. 391 
and 392. 

With p = 1.2 in Eq. (247), v a = 0.02356 t + 10.83; and two points, say at 
100 deg. y a = 2.36 + 10.83 = 13.19, and at 40 deg. v a = 0.94 + 10.83 = 11.77 
cu. ft., are enough to locate the straight air line like AB. 

For p = 1.2 lb., the boiling point is 108.02 deg. At 100 deg. the vapor ten- 
sion is 0.946 lb., at 40 deg. it is 0.1217 lb. — these from column 1 of Table II. 
Then by Eq. (248), 

v 100 = 13.19 X ]; 2 Q = 13.19 X 4.73 = 62.3 cu. ft. 

i> 40 = 11.77 X L ^ 100 = 11.77 X 1.113 = 13.10 cu. ft. 

The reciprocals of the ratios just used, namely, 

at 100 deg., ^ = 12 ~ 0- 946 = ^f = 0.212, 

at 40 deg., ^ = 1 - 2 - 2 0122 = ig 8 = 0.898, 

give air fractions, or ordinates up to the ratio curve in Fig. 392. Remember 
that these are ratios of volume quantities, reduced to and compared at the same 
pressure, not of weights. 



552 SUNDRY STEAM APPLIANCES. [Chap. XL 

(/) Quantity of Air to be Handled. — This is the most uncertain 
element in both the design and operation of a condensing plant, since 
it depends so largely upon rate of leakage. Water coming in from 
ordinary exposure to the air is likely to contain about 2 per cent of its 
own volume of free air. By the last term we mean air under atmos- 
pheric pressure and at 60 deg. fahr., of which the specific volume is 13.1 
cu. ft. to the pound and the density 0.0764 lb. per cu. ft. In what fol- 
lows all air quantities will be expressed in cubic feet of this free air, 
which has already been made the basis of Fig. 391. 

Stodola (Fourth Edition, page 549) says that we may generally 
figure on 3 to 5 kg. of air per hour per 1000 kw. of turbine capacity, 
although citing a determination (of his own) of 35 kg. per hour from a 
2000-kw. plant which was in good condition except as to leakage. Al- 
lowing 16 lb. of steam per kilowatt-hour, the average rate named (3 to 
5 kg.) becomes 0.35 to 0.55 cu. ft. of free air per cubic foot of feed 
water. Evidently, the 2 per cent, more or less, in the feed water itself 
is insignificant. 

A jet condenser will probably use something like 25 lb. of cooling 
water per pound of steam condensed. At 2 per cent by volume, this 
water will carry the free-air equivalent of about 50 per cent of the 
feed-water volume. The approximate equality here shown between 
air in cooling water and air in exhaust steam checks up very well with 
the practical rule that a jet condenser (with both these quantities to be 
handled) should have about twice as much air-pump capacity as a sur- 
face condenser of the same power rating. On this point, Mr. R. M. 
Neilson * states, for instance, that the air in the injection water may be 
less than that coming from the turbine, with moderate leakage; but 
with high vacuum (which generally means a higher ratio of cooling 
water) the former may be as much as three times the latter. The 
engine, with stuffing boxes kept well packed, is not likely to have any 
more air leakage than the turbine. 

Example 57. — Find the air-pump capacity requisite for a 1000-kw. sur- 
face condenser, to maintain a vacuum of 28 in. of mercury or an absolute pres- 
sure of 1 lb. per sq. in. 

Allowing 16,000 lb. of steam per hour, or 256 cu. ft. of feed water, we take 
45 per cent of this, or 115 cu. ft., as the volume of free air per hour. Even in a 
plain condenser like Fig. 389 the condensate will be cooled quite a little below 
the temperature of the exhaust steam, since the coldest tubes are at the bottom 
of the condenser. Let us assume that the final temperature will be 75 deg.; 
then by Fig. 391 the volume per cubic foot of free air will be about 26.5 cu. ft. 

* Factors Affecting Air Pump Capacity, Power, Nov. 29, 1910. 



§ 53 (/)] CONDENSERS AND AIR PUMPS. . 553 

The air pump will therefore have to take in 26.5 X 115 = 3051 cu. ft. per 
hour, or 51 cu. ft. per minute. 

Compare with this result an example of performance reported in Power for 
Nov. 22, 1910, page 2066. A Wheeler jet condenser, similar in type to Fig. 
394 and installed with a 2000-kw. turbine, received cooling water at 51.0 deg. 
and discharged it at 90.4 deg., maintaining a vacuum of 28.50 in. or a condenser 
pressure of 0.73 lb., to which corresponds a steam temperature of 91.5 deg. 
From assumed values of steam rate and thermal data, it was calculated that 
about 182 cu. ft. of cooling water entered the condenser per minute. At 2 per 
cent, the free air from this water is 3.6 cu. ft., and a fair allowance would make 
the probable whole amount 6 cu. ft. per minute. It was estimated that the air 
and vapor mixture might have a temperature of 65 deg. and an absolute pressure 
of 0.60 lb. in the cylinder of the air pump during suction; for which conditions 
Fig. 391 gives a relative volume of about 50 cu. ft. Then the required air- 
pump capacity seems to be 300 cu. ft. per minute, while the actual displace- 
ment was 555 cu. ft. A volumetric efficiency of 0.9 would reduce the latter to 
500 cu. ft. effective, but there remains a most decided discrepancy between 300 
and 500, throwing doubt on the assumptions as to free-air quantity and as to 
realized cooling of the air and vapor mixture. In regard to the last condition, 
we note that a rise of temperature from 65 deg. to 74 deg. would bring the re- 
quired volume above 500 cu. ft. per minute. 

(g) Countercurrent Jet Condensers. — With any reasonable 
proportioning of the internal passages for steam, pressure will be almost 
uniform throughout the enclosed space of the condenser. A similar 
uniformity of temperature by no means follows, and the last example 
has supplemented Art. (e) in showing how advantageous is the scheme 
of cooling the gas-and-vapor mixture before sending it to the air pump. 
Two typical designs in which local cooling is effected in condensers of 
the mixing class are illustrated in Figs. 393 and 394. 

The first thing to be noted in Fig. 393 is the thorough spraying of 
the cooling water and the low position of the exhaust inlet. The fine 
spray of water is heated nearly up to the temperature of the steam 
through which it falls, thus insuring a maximum absorption of heat; 
while the "air" rising from the condensed steam is cooled and dried 
by unheated spray, before passing through pipes to the top of the con- 
denser. From this opposite flow of air and of water is derived the 
name " countercurrent." Meanwhile, the air in the injection water 
has nearly all been released by simple lowering of pressure, and escapes 
without being heated at all. Above the condenser is a vertical length 
of large pipe which serves as a separator, or a quiet chamber where 
drops of water can separate from the air current (if entrained) before 
the latter goes to the dry air pump. Special features of this- design are, 
the equalizing pipe and the overflow pipe. The first gives the descend- 



554 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 

















Fig. 393. 



Large Barometric Condenser, illustration from bulletin of Allis-Chalmers 

Company. 






§ 53 (g)) 



CONDENSERS AND AIR PUMPS. 



555 



ing water current a chance to exert all the air entrainment of which it 
is capable, thus largely diminishing the service required of the air 
pump. The second insures the effectiveness of this ejector action: the 
tail pipe is so proportioned that it will be filled even by the smallest 
rate of water flow likely to occur, while at heavy loads all excess water 
goes down the large overflow pipe. 

In Fig. 394 is seen the working out, with a different form of the 
condenser and its parts, of the same ideas of thorough spraying, of 
cooling the air from the exhaust steam by unheated spray, and of allow- 
ing the air in the injection water to escape at once into cool space. 
This water is distributed by seven parallel troughs, over the edges of 
which it falls in thin streams, and splashes on the spray plates. The 
condenser is placed right beneath the turbine, making a very compact 




Fig. 394. — Tomlinson Mixing Condenser, Allis-Chalmers Company. 

for Mar. 22, 1910. 



See Power 



unit. It is served by two centrifugal pumps, on the same shaft, of 
which the larger draws water from the condenser, the smaller sends a 
stream to the air ejector shown in Fig. 401. 

Similar progressive cooling of the air pump " burden" toward exit 
is arranged for in modern surface condensers : but before enlarging upon 
this point, it will be well to take up the subject of heat transmission 
through tube walls. 

(h) Action of Cooling Surface. — The simplest case will be con- 
sidered first, and elements of complication and uncertainty introduced 
afterward. Let 

t B = temperature of steam in condenser, now assumed to be uni- 
form throughout whole space, or over all cooling surface. 
t = temperature of cooling water, rising from ti at entrance to U 
at exit. 



556 SUNDRY STEAM APPLIANCES. [Chap. XI. 

A = area of whole cooling surface of condenser, in square feet. 

K = rate of heat transmission, in B.t.u. per hour per square foot 
of surface and per degree of temperature difference be- 
tween substances on opposite sides of tube wall. 

Q — heat transferred per square foot per hour. 
Q m = average transfer per square foot, so that AQ m is the whole 
heat given up by the steam and absorbed by the water. 

S = steam condensed per hour, pounds. 

W = water used per hour, pounds. 

w = W -T- S = cooling water per pound of steam. 

We now assume K to be independent of the temperature difference 
and constant for all the surface involved. If the water temperature be 
averaged as t m , on a base of surface traversed or of length of water 
path, an equation between heat transferred and heat absorbed by 
water from t\ to h gives, 

AQ m = AK (t a -t m ) = W(t 2 - h) (249) 

The first question that arises concerns the value of t m , or the manner 
of variation of water temperature along the path of flow. For an ele- 
ment of surface at a particular temperature t, we have the equation 

QdA =K(t s -t)dA = Wdt; (250) 



whence 



W p 



= ^loger-^- 1 - .... (251) 



(t s -t) K &e * s - 
Combining Eqs. (249) and (251), 

= loge 



and 



(t a -t m )= *' k • (252) 



loge 






In Fig. 395, the full-line curves belong to this simple case, for the 
assumed temperatures t 3 = 100, £i = 70, U = 90 deg. The base is 
area A, with unity representing the whole surface traversed. Line 
DE shows the constant steam temperature £ s , curve ABC the variant 
water temperature t Eq. (251) may be written, 

A=Clog e ^4 1 ; (253) 

then if A = 1.00, the constant C becomes, with the temperature limits 
just named, 

C = 1 -f- loge 3 = 1 -*■ 1-0986 = 0.910. 




§ 53 (h)] 



CONDENSERS AND AIR PUMPS. 



557 



If the integration be carried from ti to some t (not to U), the abscissa 
of a point on curve ABC is found from 

30 



A = 0.91 log € 



100- t 



If * = 80, for instance, A = 0.91 -log e 1.5 = 0.91 X 0.4055 = 0.369, at 
B in Fig. 395. 

100 



D 


y 


*~~~ 


H 






T 








/ 












+? 








/ 

/ 
/ 
i 






B r 






5f^r 


r^ 


-^ 


r^^ 


-~"~" 


' — 2 


G 




-^"C-" 


'"?' 




«t 


w 












^^Z— 


„,-- — 




















1 























f 

80 

A 

60 
A 0.5 1.0 

Fig. 395. — Curves of Temperature Variation. 

With an arithmetic mean of h and h, the average range in this ex- 
ample would be 20 deg. ;• but by substituting in Eq. (252) we find the 

true mean to be 

20 20 100J 

^-^ = io^3 = r0986 =18 - 2deg " 

or the mean ordinate of curve ABC is 81.8 deg. fahr. 

{%) Coefficient of Heat Transfer. — In a paper on " The Trans- 
mission of Heat in Surface Condensation," by Mr. G. A. Orrok, in Jour. 
A.S.M.E. for Nov. 1910, Vol. 32, will be found an account of some 
very extensive experiments made by the writer of the paper, with a re- 
production, combination, and discussion of previous data. His con- 
clusions are summed up in the expression (with changes of symbol), 



K = C 



BR?M VV, 



\*s lm) 



i ) 



(254) 



where 
K 
C 
B 
R 



average transfer coefficient, in terms described above. 

a constant, given as 630. 

coefficient of cleanliness of tube surface, ranging from 1.0 to 0.5. 

ratio of steam richness, p s /p in terms of Art. (e) ; it is the ordi- 
nate above a curve in Fig. 392, and ranges from 1.0 to per- 
haps as little as 0.2 near the air-pump outlet. Note what a 
tremendous influence this factor is given. 



558 SUNDRY STEAM APPLIANCES. [Chap. XI. 

M = material coefficient, ranging from 1.00 with clean copper down 
to 0.55 with badly-corroded brass. 

V w = velocity of water through tubes, in feet per second, ranging 
from 1 to 11.5 in the velocity experiments: about 8 ft. is 
recommended for normal or rated working, in a paper by 
the same writer in Power for June 1, 1909, page 966. 

t s and t m have the same meaning as in the last article. 

According to Mr. Orrok's experiments, the coefficient K is in- 
versely proportional to the one-eighth power of the temperature differ- 
ence, or the rate of transfer Q varies as the seven-eighths power of the 
difference. He considers it quite close enough to calculate the mean 
range by Eq. (252), then use this mean in Eq. (254) and in getting Q 
from K. 

Continuing the conditions in the example under Fig. 395, which 
represent usual specification requirements (the most severe conditions) 
for turbine condensers, taking B = 0.75, R = 0.97, M = 0.8, V w = 8, 

we find, 

v 630 X 0.75 X 0.97 5 X 8 _ ftQ _ 
K = jg-^ = 798.5. 

And 800 for K, with a mean difference of 18 deg., gives Q = 14,400 
B.t.u. per sq. ft. of condenser surface per hour. Turning to Table 20, 
and noting that input Q (as there given) is above condenser temperature 
and that the subtraction of output W from Q gives but a little more 
heat than goes to the condenser above its own temperature, we see that 
the cooling water must take up from 950 to 1050 B.t.u. per pound of 
exhaust, or say 1000 B.t.u. as a general average. Then the rate just 
deduced would call for a little more than 1 sq. ft. of surface per kilowatt 
or about 0.7 sq. ft. per horse-power. Twice this amount of surface has 
generally been considered a close allowance, but the tendency is toward 
a more definite control of the internal operation of the condenser, with 
resulting higher efficiency. 

(j) The Performance of Surface Condensers is well represented 
by Table 26. Approaching this member of the plant from without, the 
prominent quantities are those given in columns 2 and 5. Seven 
pounds per square foot per hour seems to be a good average for the 
condensation rate, rising to ten in Nos. 11 to 15; the very high rates in 
Nos. 2 to 5 belong to experimental apparatus. 

The transfer rate Q, equal to w(t 2 — h) and to K(t 3 — t m ), is not in 
itself alone a good criterion of efficiency, but must be analyzed into its 
factors. With an unlimited supply of cold water, so that the difference 
(t B — *m) is made large by having the range (Z 2 — h) short and low down 






§ 53 (J)) 



CONDENSERS AND AIR PUMPS. 



559 



on the thermometer scale, the condenser deserves no great credit for a 
high value of Q: but a good vacuum with but a moderate supply of com- 
paratively warm water can be maintained only by high efficiency in 
heat transmission and in air removal. Good working along both these 
lines is most effectively shown by a small value of the difference (t a — t 2 ), 
in column 11, coupled with a high value of the transfer coefficient K. 

An ideal condenser would raise the outgoing water to the tem- 
perature of steam saturation for the exhaust pressure p , making this 
pressure (or the realized vacuum) depend wholly upon the initial tem- 
perature h and the quantity ratio w of this water. A large difference 
between t s and U generally means poor conduction of heat, due to foulness 
of tubes or to excessive presence of air in the condenser. In extreme 
cases, there may be so much air that even near the exhaust inlet the ex- 
isting temperature t in the steam space will be appreciably less than t a 
for p - The influence of air-pump capacity is strikingly shown in tests 
2 and 3 with turbine No. 9, by the decrease of (t s — t 2 ) with rise of p 
and consequent shrinkage in the volume of air to be handled; displace- 
ment remaining (presumably) nearly the same, the pump is far more 
effective at the higher pressure. Unusually complete air removal is 
probably the chief reason for the high efficiency, in heat transfer and 
in vacuum maintenance, of the type of condenser represented by Nos. 
11 to 15 in Table 26. 

The difference (t s — t w ) in column 12, or the drop from exhaust 
steam to water of condensation, is of some economic interest when the 
condensate is to be used as boiler feed. Chiefly, its high or low value 
is a characteristic of different types of air-pump arrangement. With 
a plain wet vacuum pump, handling water and air together, t^ must be 
lowered well toward t\, to keep down the volume of uncondensed vapor. 
With a separate dry-air pump, the liquid condensate may be kept 
warmer, by diverting it from the coolest tubes near the bottom of the 
condenser, and using these to chill and dry the air and vapor mixture. 
A negative value of this difference, physically an impossibility, throws 
doubt on the accuracy of pressure measurement. 

The ideas in the last two paragraphs apply equally to the jet con- 
denser, and with some changes of form these statements might have 
been added to Art. (g). Ideal action would give the water current 
(mixed cooling water and condensed steam) the temperature t B of the 
entering exhaust. With combined evacuation, as in Figs. 387 and 388, 
the whole mixture must be cooled well below t s , to diminish the vapor 
volume. But with the principle embodied in Figs. 393 and 394, the 
water current may be kept almost as warm as the steam — witness the 
performance quoted in Example 57. 



560 
Table 26 



SUNDRY STEAM APPLIANCES. [Chap. XI. 

Performance of 







l 


2 


3 


4 


5 


6 


7 


8 


9 


10 


No. 


Old 

No. 


3 
C . 

O © 

^_ o 
o3<£2 


S a 

o3 


II 

(-GO 


03 


o 

45 © 

ft£ 

s » 
His 
o<5 


u 
© 

» 

w o 

©HH 

ft 


© 
u 

3 . 

73 © 

m 43 
Oi 3 
U A 

Ph o 

©in 
c . 

%4 


u 

3 

a 

© 
ft . 

s 


© 

u 

3 
-*> 
03 . 

&©■ 

S^ 
.2 


© 

H 

3 

©s 

hC 

■ _, o 

03 


e 
o 

O 03 
© *j 

£CO 

03 <u 

© e 

ftg 






+3 ** 

o 


02 


£ 


.So 


03 

© 


o 
O 


e3 
© 

m 


"S 


a 


g^3 
© 






A 


5 


W 


h~ h 


Q 


Po 


h 


h 


h 


U 


1.1 


953 


170 


4.19 


64.1 


15.5 


4160 


0.68 


89.2 


51.0 


66.5 


71.9 


2 


958 


< t 


6.47 


41.7 


22.6 


6100 


0.98 


101.2 


50.6 


73.2 


94.1 


3 


963 


it 


9.58 


28.2 


34.2 


9230 ' 


1.65 


119.2 


50.1 


84.3 


117.8 


4 


968 


a 


10.94 


24.8 


39.3 


10660 


2.07 


127.4 


50.0 


89.3 


128.4 


2.1 


987 


101 


17.22 


31.8 


30.0 


16440 


0.67 


88.9 


45.3 


75.3 


90.0 


2 


991 


c < 


18.81 


13.3 


73.0 


18250 


1.95 


125.4 


45.7 


118.7 


128.9 


3.1 


1014 


101 


12.52 


45.9 


22.0 


12640 


0.51 


80.2 


46.0 


68.0 


76.3 


2 


1035 


i I 


18.30 


14.2 


71.5 


18560 


1.71 


120.5 


42.5 


114.0 


121.9 


4.1 


1055 


62 


35.6 


26.0 


35.9 


33220 


0.96 


100.4 


41.3 


77.2 


101.3 


2 


1061 


<< 


27.8 


14.4 


66.3 


26530 


2.16 


129.0 


41.7 


108.0 


132.0 


5.1 


8 


307 


7.89 


30.2 


34.0 


8090 


0.70 


90.0 


50.4 


84.4 


65.7 


2 


6 


1 1 


7.91 


49.8 


20.8 


8210 


0.52 


81.9 


50.4 


71.2 


54.0 


3 


3 


n 


13.12 


24.0 


43.7 


13780 


1.00 


102.0 


50.4 


94.1 


79.5 


4 


1 


u 


13.03 


51.4 


20.8 


13930 


0.56 


82.3 


50.4 


71.2 


58.5 


6.1 


4-7 


962 


7.25 


20.2 


54.4 


7960 


1.67 


119.8 


.50.5 


104.9 


61.2 


2 


4-8 


ii 


7.13 


24.9 


43.4 


7700 


0.88 


97.9 


50.5 


93.9 


71.4 


3 


4-12 


u 


7.14 


39.2 


27.3 


762.0 


0.56 


82.3 


50.5 


77.8 


64.4 


4 


411 


it 


7.42 


36.9 


29.0 


7930 


1.06 


104.6 


71.9 


100.9 


87.3 


7.1 


6-6 


959 


6.15 


40.4 


26.1 


6480 


0.78 


93.6 


50.8 


76.9 


71.1 


2 


6-1 


< i 


7.99 


32.6 


32.9 


8580 


0.77 


93.2 


50.8 


83.7 


65.9 


8 


101 


1883 


6.80 


98.0 


10.8 


7200 


0.52 


80.6 


49.1 


59.9 


68.9 


9.1 


58 


25000 


3.26 


153.0 


6.3 


3140 


0.48 


78.4 


33.2 


39.5 


53.9 


2 


54 


<< 


7.06 


77.1 


14.3 


7780 


0.46 


77.1 


33.5 


47.8 


57.3 


3 


14 


n 


7.05 


78.6 


13.6 


7530 


0.80 


94.5 


73.0 


86.6 


86.4 


4 


38 


i i 


9.50 


53.5 


19.6 


9950 


0.74 


92.0 


37.7 


57.3 


71.2 


10.1 


I 


4520 


3.52 


71.3 


14.6 


3660 


0.44 


75.8 


59.5 


74.1 


69.8 


2 


II 


<r 


4.48 


52.7 


19.1 


4510 


0.53 


81.4 


60.6 


79.7 


82.6 


3 


III 


u 


6.25 


54.6 


19.4 


6620 


0.67 


88.8 


57.6 


77.0 


81.0 


11 


1044 


2205 


11.2 


70 


14.3 


11220 


0.38 


71.5 


52.4 


66.7 


68.8 


12 


1007 


3200 


11.0 


77 


13.0 


11000 


0.82 


95.3 


76.5 


89.5 


89.. 8 


13 


1008 


3350 


10.4 


71 


14.0 


10400 


0.79 


94.1 


72.8 


86.8 


87.0 


14 


1102 


3350 


11.5 


80 


12.5 


11540 


0.88 


97.6 


82.4 


94.9 


96.5 


15 


991 


1800 


8.8 


54 


18.5 


8800 


1.58 


117.7 


92.8 


111.3 


110.1 



Columns 2 to 5 are tied together by the relation Q = sw (t 2 — ti). 

Columns 6 to 10 are observed quantities, except that steam temperature U is taken from the table, for p . 

The meaning of the temperature differences in columns 11 and 12 is explained in Art. (j). 

The factor in column 13 is used in getting the mean range (ts — tm), according to Eq. (252). 

In column 15, K is the quotient [Q -r (t B — tm)]. 



§ 53 (j)] 



CONDENSERS AND AIR PUMPS. 



561 



Surface Condensers. 



Table 26 



11 


12 


13 


14. 


15 


16 






£ 

ri- 
43 a> 




|| 


a 
^ o 






w$. 


COS"; 


T T 




tjE 


•■H O 

O 0) 






o O 


M 


<C a> 

fig 


® S3 


> 8. 


References, Notes, etc. 


5JJ> 


a>^3 


_o 


c <° 


a m 








33 § 




^ 


. 0) 


1 




Q § 


A 




B 








< 3 — <2 


i 3 — £w 




*s ^m 


K 


^w 




22.7 


17.3 


0.521 


29.8 


114 


0.8 


From paper by Prof. R. L. Weighton, 


28.0 


7.1 


0.592 


38.2 


160 


0.8 


Trans. Inst. Nav. Arch., 1906, Vol. 48, 


34.9 


1.4 


0.683 


50.1 


181 


0.8 


122-156. Experiments at Armstrong 


38.1 


-1.0 


0.709 


55.4 


193 


0.8 


College, Glasgow. No. 1, old-type plain 
condenser, f in. tubes, 4 ft. long, 5 


13.6 


-1.1 


1.166 


25.7 


640 


4.5 


passes. No. 2, " contraflo " condenser 


6.7 


-3.5 


2.476 


29.5 


618 


2.1 


about as in Fig. 397, f in. tubes, 4 ft. 
long, 4 passes. No. 3, same as No. 2, 


12.2 


3.9 


1.037 


21.2 


597 


4.6 


but with separate dry air pump. No. 4, 


6.5 


-1.4 


2.485 


28.8 


644 


2.0 


like No. 2, but with tube length short- 
ened to 2.5 ft. 


23.2 


-0.9 


0.932 


38.5 


864 


4.6 




21.0 


-3.0 


1.426 


46.6 


570 


2.0 




5.4 


24.3 


1.966 


17.4 


465 


1.3 


From paper by Prof. E. Josse, Zeit. 


10.7 


27.9 


■1.079 


19.3 


425 


2.2 


Ver. deutsch. Ing., 1909 I, Vol. 53. No. 


7.9 


22.5 


1.878 


23.3 


591 


1.7 


5, special experimental condenser, 


10.1 


23.8 


1.061 


19.6 


710 


3.2 


water channel of changing cross section, 
13.93 ft. long, tubes 0.59 in. diam. No. 


14.9 


58.6 


1.953 


35.4 


223 


0.7 


6, tubes 0.71 in. diam., 2 passes, length 


4.0 


26.5 


2.281 


17.5 


439 


0.8 


15.1 ft. No. 7, first test, plain tubes; 


4.5 


17.9 


2.470 


14.0 


555 


1.3 


second test, " spiral " (helical) baffle 


3.3 


16.9 


1.535 


12.7 


625 


1.2 


strips in tubes. No. 8, condenser in 
regular service. 


16.7 


22.5 


0.940 


27.7 


235 






9.5 


27.3 


1.497 


22.0 


390 






20.7 


11.7 


0.419 


25.8 


279 






38.9 


24.5 


0.270 


41.7 


75 


4.2 


Turbine-base condenser Fifty-ninth 


29.3 


19.8 


0.399 


35.6 


218 


4.6 


Street Power House, New York: with 


7.9 


8.1 


1.044 


13.1 


575 


4.7 


turbine No. 50 in Table 20 and engine 


34.7 


20.8 


0.445 


43.8 


227 


4.3 


No. 27 in Table 13. 


1.7 


6.0 


2.261 


6.4 


568 




Balcke condenser, Stodola IV, 551, 


1.7 


-1.2 


2.503 


7.6 


592 




556; air and vapor guided over coldest 


11.8 


7.8 


0.971 


20.0 


331 




tubes before going to air pump. 


4.8 


2.7 


1.381 


10.3 


1090 


8.6 


Condensers with Parsons vacuum 


5.8 


5.5 


1.177 


11.1 


1090 


7.1 


augmenter: from table of data pre- 


7.3 


7.1 


1.072 


13.1 


790 


6.2 


sented by Mr. R. J. Walker, in discus- 


2.7 


1.2 


1.728 


7.2 


1590 


7.4 


sion of paper by Mr. D. B. Morison, 


6.4 


7.6 


1.358 


13.6 


645 


6.7 


Trans. Inst. Nav. Arch., 1908, Vol. 50, 

page 169. In these tests the steam rate 

it absorbed Q, by assuming 1000 B.t.u. 


was not given, but i 


s derived from hea 


from the pound of st 


earn. 









562 SUNDRY STEAM APPLIANCES. [Chap. XI. 

(k) Efficiency of Cooling Surface. — Some brief discussion of 
the influences given place in Eq. (254), partly a review and summary, 
seems appropriate. Concerning cleanliness and material, as bearing 
on conductivity, it is enough to say that the condition of the surface — 
whether clean metal or coated with an insulating film or sheathing — 
is far more important than the metallic composition of the body of the 
tube : in other words, for the metallic wall, surface resistance is far greater 
and more widely variable than internal resistance. As between the 
two types of steam machine, the turbine has the advantage over the 
engine that it does not send heavy oil into the condenser, likely to coat 
the tubes with grease on the steam side. 

That water velocity has a considerable influence is readily accounted 
for by the fact that water is a poor conductor, and must be heated by 
convection. The tendency is to form a thin layer of warm water about 
a cooler core, within the tube. Rapid flow, or the insertion of baffles 
as in No. 7 of Table 26, keeps the current well stirred up, continually 
bringing fresh portions into contact with the walls, Also, with dirty 
water, swift flow scours out the tubes and keeps them clean. A limit to 
economical velocity is imposed by the rapid rise of resistance and of 
work by the circulating pump, since the pressure required varies as the 
square of velocity. 

The poor conductivity of a layer of water accounts for the disad- 
vantage of " water drowning": in a large condenser, the heavy shower 
from above covers the lower tubes so thickly that steam has poor access 
to them. The scheme of partial drainage, illustrated in Figs. 396 and 
397, is intended to overcome this difficulty and keep the tubes compara- 
tively dry. 

The deadening effect of air drowning has been alluded to in the last 
article, and in Fig. 395 is tentatively represented by the dotted curves 
AFC and GH. In the active space near the steam inlet, flow of steam 
is so strong that air cannot accumulate; but the cooler tubes toward 
the air-pump outlet will be surrounded by a mixture of increasing air 
richness. To show the consequent low conduction, curve AFC is made 
to rise very slowly at first; and while the cooling of the air mixture does 
not involve much heat abstraction, the drop from H to G is spread over 
a considerable length of base. The curves are wholly illustrative, not 
being based on any quantitative investigation. The practical inference, 
from the viewpoint of design, is that a relatively large amount of surface 
will be required for the operation of cooling and drying the air-and- vapor 
mixture. 

(I) Various Surface Condensers. — Fig. 396 illustrates the in- 
troduction of drainage plates or " rain plates," slightly pitched from 



§ 53 (I)] 



CONDENSERS AND AIR PUMPS. 



563 



the middle toward the walls, down which the water runs instead of fall- 
ing on the tubes below. As shown in the plan at B, large holes through 
the plates give passage to steam, and these holes are " staggered " in 
sequence, so as to promote circulation. Evidently, this arrangement 
will largely prevent cooling of the water of condensation. Note the 
passages formed between three groups of tubes in the first section; these 




Fig. 396. — Wheeler Dry-tube 
Condenser. 



Fig. 397. — Early Form of 
Contraflo Condenser. 



give better access of steam to the second section, and insure high ac- 
tivity in the latter. Some such scheme of permitting freer flow among 
the higher tubes is now quite common. 

The pioneer design * embodying the idea of partial drainage, with 
the double purpose of not flooding the lower tubes and of delivering 
warm water, is shown in Fig. 397. The free spaces at the sides, be- 
tween tube sections and formed by swelling out the sides of the shell, 
are intended to promote uniform, parallel flow of steam. Note the very 
distinct separation of air and water; the latter goes out at A, after 
thorough cooling in the lowest tube section, while the water runs into 
a small reservoir at one end (from sections B and C through the pipes 
shown), whence it is withdrawn at C. This was an experimental con- 
denser: in working designs the shell is of simple cross section, and in- 
clined baffle or guide plates are interposed among the tubes, so as to 
give partial drainage and to make the steam current flow in a definite 
channel of rapidly decreasing cross section. 

Figure 398 shows a device of which the effectiveness has been fully 
shown in the latter part of Table 26. A steam jet S exerts a strong 

* That of Weighton; see reference from Nos. 1 to 4 in Table 26. The name 
"contraflo," used as a trade name, is not based on countercurrent action, but on a 
special effort to spread the steam current sidewise at entrance, and then have it 
flow squarely across and among the tubes. 



564 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 



ejector action at D, drawing air and vapor from the main condenser. 
The small auxiliary condenser cools the ejector discharge, liquefying all 
excess of steam, and delivers it to the air-pump suction at F. With the 
increases of pressure represented by the hydraulic head h, the mixed 
condensate is easily handled by pump of moderate capacity. The 



WATER OUT 




Fig. 398. — The Parsons Vacuum Augmenter. 



steam consumed by the ejector is said to be about one per cent of the 
normal consumption of the turbine. 

As more or less special types may be mentioned the following: 

The feed-heater condenser, in which the boiler feed is passed through 
a top section of tubes, above those through which cooling water is 
pumped. 

The water-works condenser, with steam inside of the tubes and 
water outside, in order to get a smaller resistance to flow of water. 
This is placed in a bypass on the suction pipe of the pumping engine, 
and the needed diversion of water is secured and varied by a butterfly 
valve in the main pipe. 

The " countercurrent " condenser, with steam entering at the bot- 
tom and cooling water at the top. The condensation water is fully 
warmed by showering down through entering steam, while the dry-air 
pump draws from the top of the condenser. Since air is heavier than 
steam, and cooling causes a further increase of density, this scheme is 
somewhat illogical. 

It may be remarked that terms describing relative directions of 
flow have a conventional and limited meaning when used in connection 



§ 53 (I)] 



CONDENSERS AND AIR PUMPS. 



565 



with the condenser. All jet condensers have parallel flow of cooling 
water and condensed steam, all surface condensers opposite flow of 
steam and water; so that " countercurrent " and its implied opposite 
refer to the direction of air flow. 

(m) Air Pumps. — Typical simple, combined-service or wet vacuum 
pumps are shown in Figs. 387 and 398, the latter not specifically belong- 
ing to the condenser which it accompanies. The vertical pump, single 
acting, has three sets of valves, while the horizontal pump has but two 
sets. In the latter the working " piston " is really a water surface, 
which rises and falls in the chambers H, H. Air-pump valves are of 
the flat disc form in Figs. 387 and 399, not cone-seated as sketched in 
Fig. 398. 

An improved vertical pump with but one set of valves, or " suction 
valveless," is shown in Fig. 399. A certain amount of water always re- 
mains in the bottom of the cyl- 
inder, and more flows in while 
the piston rises and during most 
of the down stroke. The lower 
face of the piston P is conical, 
quite closely fitting the cylinder 
bottom; then as it comes down 
the standing water is forced out, 
impelled around the curved sur- 
face W, W, and shot in through 
the ports. This spray of water 
will exert some injector action 
upon the air present, helping 
to fill the suction space. The 
pump is, of course, crank driven, 
since the stroke of the piston 
must be very definite. 

As already remarked, the dry-air pump is, in form and working, 
very much on the lines of the common air compressor. Its function is 
to receive a mixture of air and steam at from 0.5 to 1.5 lb. absolute and 
compress it to atmospheric pressure. Often the cylinder is water- 
jacketed, since so great a range of compression involves a good deal of 
heating; and sometimes there are two stages of compression, in suc- 
cessive cylinders. The inlet valves are commonly operated mechani- 
cally, to save suction vacuum. 

in) Clearance and Volumetric Efficiency. — The purpose of 
the air pump, of either class, is to remove as large a volume as possible 
of the air and vapor coming to it; and the greatest obstacle in the way of 




Fig. 399. — The Edwards Air Pump. 



566 SUNDRY STEAM APPLIANCES. [Chap. XI. 

efficiency is clearance — using this term in the same sense as with the 
engine cylinder. Suppose, for example, that a dry-air pump has a 
pressure range from 0.75 lb. to 15 lb., or a ratio of 1 to 20. Under the 
law pv = C, the compressed volume would be 0.05 of the suction vol- 
ume; but really the compression will be quite nearly adiabatic, or 
enough so to increase this final volume to 0.09 or 0.10. If the clearance 
is, say, 3 per cent of the displacement, only 0.65 to 0.70 of the charge 
will be expelled, the remainder expanding behind the piston as it returns, 
spoiling the suction vacuum of the pump or delaying the indraft of fresh 
charge. The volumetric efficiency, or the ratio of actual suction vol- 
ume to displacement, will be only 65 to 70 per cent. 

In wet-air pumps, the effect of clearance is largely neutralized by 
the presence of water. In the three-deck vertical pump, like Fig. 398, 
the piston will always carry enough water above it to fill the clearance 
space at the top of the cylinder, so that all air will be expelled. During 
the down stroke pressure is equalized on the two sides of the piston, 
barring valve resistance, so that even if the water above the piston has 
received heat of compression, its vapor tension cannot diminish volume 
capacity. On the last point the single-acting pump has an advantage 
over all those in which the same side of the piston, or the same moving 
surface, is active in both suction and compression. Even though all air 
be expelled from the pumps of Figs. 387 and 399, vapor from the water 
will fill or tend to fill the suction space, and will have to be condensed 
or compressed by the entering charge. The spray injected by the 
piston action of the Edwards pump will be more active than a plain 
water surface in thus condensing vapor. 

The introduction of water to fill the clearance space of a dry-air 
pump would be a very poor expedient, because this water would be 
warmed during compression and would have a high vapor tension. 
The best scheme is to use a " snifting " valve, which controls a passage 
connecting the two ends of the cylinder, and is opened (mechanically) 
soon after the crank passes each dead center and kept open for a short 
time. Then the high-pressure clearance content at one end passes into 
the other end, where pressure is low because compression has just 
begun. With this arrangement, the volumetric efficiency may rise as 
high as 95 per cent. 

(o) Water Ejectors. — In Fig. 400, the point of special interest is 
the air pump. As to the condenser in general, water enters at A and is 
sprayed downward from an annular distributor C. The whole prod- 
uct of mixing and condensation, in a stream filling the large funnel or 
nozzle, sweeps into space E, where the air separates and is drawn off 
through pipe K. A plain centrifugal pump takes water from the con- 



§ 53 (o)] 



CONDENSERS AND AIR PUMPS. 



567 



denser; and on the same shaft with it is the impeller of turbine pump P, 
which sends a stream of cool water into the ejector nozzle. The stream 
is delivered in layers, or broken into spray, and the interstices among 
drops being necessarily filled with their surrounding atmosphere, this 




SECTION M.-M. 
THROUGH WATER PUMP. 



Fig. 400. — The Leblanc Condenser and Pumps. From Bulletin of Westinghouse 

Machine Company. 

air from the condenser is carried out by and with the water. Partly 
by suction of the vacuum, partly by the impeller, the current is given 
sufficient velocity to expel it against outside pressure. If the cold 
water tank is not high enough for flow to the pump by gravity, steam 
is let in at L when starting up. This air pump can equally well be used 
with a surface condenser. 

A fundamentally equivalent device, although quite different in 
form, is shown in Fig. 401. Water, from a special centrifugal pump, 



568 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 




Fig. 401. — Tomlinson 
Air Ejector, with con- 
denser in Fig. 394 



comes in at W and is discharged through a ring nozzle in a hollow coni- 
cal jet or sheet. Air from A has parallel admission both inside and 

outside of the cone of water. The latter breaks 
into spray, yet with enough velocity for self- 
expulsion, and air is mixed with and carried out 
by this broken stream. 

If water is not plentiful, the same supply may 
be used over and over again in these air pumps. 
The scheme is essentially that of the old ejector 
condenser, but with the advantage that the whole 
condensate need not be cooled to the low tem- 
perature necessary for effective air removal at 
high vacuum. Devices of this class are not sub- 
jected to the definite volumetric limitations of 
piston pumps. 

(p) Power Consumed by Condenser Pumps. 
— With steam-driven pumps, this is a rather in- 
determinable quantity; and if the exhaust from 
these auxiliaries be used to heat the feed water, their power cost is al- 
most zero, as shown in § 26 (g), page 235. With motor drive for the 
pumps, the power consumed is very easily measured, and is to be de- 
ducted from gross output. Of the turbines in Table 20, we have the 
record that the 4000-kw. unit listed as No. 35 required 60 kw., or 1.5 
per cent of rated power for the condenser pumps: and the 1500 kw. 
condenser plant, No. 10 in table 26, consumed 19 kw. in the same 
service. The average range in large and well-kept plants is probably 
from 1.3 to 2 per cent of the rated output, varying hardly at all with 
degree of loading. 

(q) The Cooling Tower. — When but a scanty supply of water is 
available, some plan of artificial cooling and repeated use must be 
resorted to. This cooling is effected by exposing a large surface of 
warm water to a current of air and thus encouraging vaporization, the 
latent heat for which will come from the water itself. The weight of 
vapor formed and carried off by the air is about equal to that of the 
steam condensed, which relation determines the amount of make-up 
water required. The simplest scheme is to use a large pond, if at hand, 
discharging warm water into one end, drawing cool water from the 
other; the first advance upon this is to spray the water upward in 
fountain jets when discharging into the pond; but under common space 
limitations a cooling tower must be added to the plant. 

This tower is a circular or rectangular shell of light plate — in effect, 
a chimney stack much shortened vertically (20 to 40 ft. high) and 






§ 53 (q)] CONDENSERS AND AIR PUMPS. 569 

very much enlarged laterally. At the top is a set of distributing 
troughs, to which the water from the condenser must be pumped; from 
these it trickles down over "mats" made of wooden slats or of woven 
wire screens, which fill the space within the tower. Sometimes nat- 
ural " draft" is depended upon for air circulation, but oftener fan 
blowers, of the helical or screw-propeller type, are installed. Of course, 
the capacity of a cooling tower is most severely taxed in warm and 
damp weather, when the air is so nearly loaded (saturated) with nat- 
ural moisture that it can take up little more. For a good description 
and discussion of this apparatus, see paper by Mr. J. R. Bibbins on 
" Cooling Towers for Steam and Gas-power Plants," in Trans. A.S.M.E., 
1909, Vol. 31, 725. 

A combination of the cooling-tower idea with the surface condenser 
has been thought of and tried — see, for instance, Trans. A.S.M.E., 
Vol. 14, 690. This self-cooling surface condenser consists of a nest of 
pipes, with steam inside, water trickling down outside, and air blown 
over the water-coated surfaces. The scheme is workable, but effi- 
ciency of heat transfer is low, hence a large amount of cooling surface 
must be provided; and the construction is necessarily such that both 
cost and space occupied per square foot of surface will be high. 

Example 58. — Suppose that a cooling tower plant, when handling water 
at the rate of 25 lb. per pound of steam condensed, returns it at 75 deg. fahr., 
and that the effective capacity of the air pump is 0.7 cu ft. per pound of steam. 
What vacuum may be expected? 

Let us assume that the. engine uses dry-saturated steam at 135 lb. abs. and 
requires 13.5 lb. of steam per horse-power-hour. The total heat of this steam is 
1193 B.t.u., and the heat converted into work per pound is 2545 -5- 13.5 = 
196 B.t.u. With a reasonable allowance for radiation, we may say that the 
total heat of the steam coming to the condenser will be about 975 B.t.u. 

If the condenser is of the jet type, all of this heat above 75 deg., or 975 — 43 
= 932 B.t.u., will go to raise 26 lb. of water (cooling water plus condensed 
steam) to the final temperature t 2 ; then 

U - k = t 2 - 75 = ^ - 34.8, 
2o 

and t 2 = 110 deg. To this corresponds an absolute pressure of 1.27 lb., which 
is the lower limit of the attainable, so that the ideal vacuum is 

29.92 x 147 ~ 1,27 = 29.92 x ^^ = 27.3 in. mercury. 

Now 0.7 cu. ft. of displacement per pound of steam is equivalent to 0.7 x 
62.4 = 43.7 cu. ft. per cubic foot of feed water. Let us assume further that 
the free-air volume of the air to be removed is equal to the volume of the feed 
water — compare Art. (/). In Fig. 391, on the ordinate at 110 deg., 43.7 cu. ft. 



570 



SUNDRY STEAM APPLIANCES. 



[Chap. XI. 



interpolates at about 1.65 lb. pressure. This is then the pressure to be expected 
if the air and vapor mixture must be removed at the full temperature of 110 deg. 
But suppose that by local cooling this mixture is reduced say to 90 deg. 
before it goes to the air pump; then on the 90-deg. ordinate of Fig. 391 a vol- 
ume of 44 cu. ft. is found to correspond with a pressure of about 1.06 lb., while 
the volume at 1.27 lb. is only about 28 cu. ft. If the air-pump displacement 
is in excess of the volume of vapor-saturated air at the temperature existing, 
the extra space will be filled by excess of vapor, drawn from the water at that 
temperature. With as little as two-thirds of the displacement named, at the 
temperature named, ideal vacuum should be realized. With a surface con- 
denser and an equivalent effectiveness of air cooling, the condenser pressure 
would depend upon the steam temperature t 3 as related to the final water 
temperature t 2 ; on this point, refer to Table 26, and note that (t a — t 2 ) may be 
as little as 5 deg. 



§ 54. The Rotary Engine 

An Immense Amount of Invention and ingenuity has been ex- 
pended upon the problem of devising a machine in which the static- 
pressure cycle could be applied to a rotating instead of a reciprocating 
working element. Inherent difficulties of the first magnitude have kept 
these efforts from success, while the advent of the turbine has satisfied 
the demand which they were intended to meet. A description of the 
various rotary engines that have been patented would belong rather to 

the study of mechanism than to practical 
steam engineering; and to illustrate the gen- 
eral principle of action we shall use but the 
one simple type outlined in Fig. 402. 

In this machine steam enters continually 
at S and escapes at E, only a plain throttle 
valve in the inlet pipe being needed to control 
the flow. Sliding vanes or pistons, P, P, P, 
project from the rotor R and touch the casing 
C, furnishing the moving surface upon which 
the working steam force acts. Some simple 
Fig. 402. — Outline of Typi- contrivance, such as a circular groove in the 
o ary ngme. ends of the casing and projections on the 

vanes, must be added in order to keep the latter out against the casing. 
This particular scheme has the fault that it makes absolutely no 
provision for expansion of steam below the inlet pressure, which puts 
it in a class with the small direct-acting steam pump. Better inven- 
tions have met this requirement to some degree, although far less 
effectively than the piston engine. But the great and determining 




§ 54] THE ROTARY ENGINE. 571 

drawback has been the inability to hold steam, or the tendency of the 
machine to excessive leakage. The circular piston, moving in its 
cylinder with a broad contact, is the simplest possible working element 
for the static-pressure cycle, and it is hard enough to keep the piston 
tight. The rectangular vane, with narrow contacts and variant rub- 
bing speed at different points of its perimeter, cannot be made and 
kept steam-tight; and there is a further chance for leakage between the 
ends of rotor and casing. As regards thermal wastes, it is evident that 
a considerable portion of the metal surface which the steam touches is 
exposed alternately to high and low temperatures. Further, since the 
machine develops its power by the combination of a small driving force 
with a high velocity, the rubbing friction due to an attempt to keep 
the piston tight will absorb an excessive amount of power. These un- 
avoidable bad features have completely overshadowed the advantages 
of compactness and freedom from shaking force. 



APPENDIX 



TABLES OF THE PROPERTIES OF STEAM 
A. List of Tables and Diagrams 

Table I. Temperatures for Various Pressures. — Since Table 
II has temperature for the argument, Table I gives the temperatures 
corresponding to equally spaced and numerically simple values of 
pressure: to be used before entering Table II, when pressure is the 
initial quantitj^. Pages 578 and 579. 

Table II. Principal Steam Table, for the properties of saturated 
steam (columns 3, 4, and 5 for superheated steam). This table covers 
at one-degree intervals the range from 32 deg. to 550 deg. fahr., and 
extends at ten-degree intervals to the critical temperature, which is 
taken as 689 deg. Pages 580 to 601. 

Table III. Supplementary Steam Table. — This contains some 
regularly used reference columns in which ten-degree spacing is close 
enough, also certain columns which find their purpose in the illustra- 
tion rather than the application of the properties of steam. Pages 602 
and 603. 

Table IV. Temperature Factor / t . This extends into the high- 
temperature range the quantity given in column 5 of Table II, to be 
used in calculating the specific volume of superheated steam. Page 603. 

Table V. Pressure Factor / p . — This covers the range of high 
pressures, above the field of application of formula (65), § 12 (i). Page 
603. 

Table VI. Specific Volume of Superheated Steam. — Diagram: 
vertical base, pressure on a scale uniform for saturation temperature; 
principal scale for horizontal ordinate (inclined ruling), temperature 
fahrenheit; secondary scale (vertical ruling), degrees of superheat. The 
curves are lines of constant volume, and the horizontal lines of con- 
stant pressure are divided for equal volume increments. Pages 604 
and 605. 

Table VII. Total Heat of Superheated Steam. — Diagram: 
vertical base, pressure on a uniform scale; the horizontal ordinate is 

573 



574 THE STEAM ENGINE AND TURBINE. 

total heat h under constant pressure — see § 13 (i). Curves marked 
TT are lines of equal temperature or isothermals; those marked SS are 
lines of equal superheat. Pages 606 to 610. 

Table VIII. Entropy of Superheated Steam. — Diagram: verti- 
cal base, temperature fahrenheit; horizontal ordinate, entropy n above 
32 deg. fahr., acquired in the reception of total heat h. The constant- 
entropy lines are inclined, to economize space. Principal curves are 
for operation of heating under constant pressure, at the pressure cor- 
responding to each ten-degree point of temperature on the saturation 
line: at top of diagram is a scale of corresponding pressures for these 
curves. The cross curves show equal superheats, at each fifty degrees 
above saturation. Pages 611 to 615. 

B. Alphabetical List of Symbols for Steam Quantities, 

With Definitions of the Quantities and Reference 
to Explanations in the Text, nearly 
all in Chapter III. 

Steam-table headings in heavy type. 

All volumetric and thermal quantities are per pound of substance, whether 
water, steam, or mixture. 

A The heat equivalent of work, or the value of one foot-pound 

in B.t.u., equal to 1/778 or 0.001285; used in the external- 
work expression APv. See Eq. (3), page 35. 

AJPu Table III, column 8. External work of vaporization; §13 (/). 

AJPtv Table III, column 7. External energy of the liquid; § 13 (g). 
In general, if a volume-increase v (cu. ft.) takes place under 
a constant pressure p (lb. per sq. in.), the work done is 144 pv 
or Pv ft. lb., using P for pressure in pounds per square foot: 
then APv is the heat equivalent of this work, in B.t.u. When 
making calculations, it is best to use 144 Apv or 0.185 pv. In 
APu and APw, u and w are particular volume symbols, as 
defined below. See § 7 (d). 

a Table II, column 11. Entropy of the liquid; Isee § 13 (Z), 

b Table II, column 12. Entropy of vaporization ;J also N below. 

c Specific heat, in following particular values. 

c p Specific heat of superheated steam under constant pressure; 

§ 13 (h) and Fig. 46. 

c v Specific heat of superheated steam at constant volume; 

§ 13 (fc). 

c w Table III, column 6. Specific heat of water; use also plain 

c;§13_(a).^ 

d Density, in pounds to the cubic foot. 



APPENDIX. 575 

Density of saturated steam, the reciprocal of the specific 
steam volume s; § 12 (c). 

d w Table III, column 3. Density of water at temperature t 

and pressure p as in columns and 1, or weight of one cubic 
foot in pounds; § 12 (c). 

/ p Table V. Pressure factor, to be used with f t in calculating 

the specific volume of superheated steam, as explained in § 12 
(i). This supersedes Eq. (65) at 900 lb. pressure. 

ft Table II, column 5, and Table IV. Temperature factor, to 

be used with / p in calculating the specific volume of superheated 
steam; § 12 (i). 

H Table II, column 8. Total heat of saturated steam, dry or 

of the quality 1.00, formed under a constant pressure p from 
water at 32 deg. fahr.; § 13 (c). 

h Table VII. Total heat of superheated steam; § 13 (i) This 

is also used as a general symbol for the total heat (under con- 
stant pressure and above 32 deg.) of steam of any quality or 
condition — see § 13 (d). 

h s Heat added to the pound of steam in superheating; § 13 (h). 

I Internal work or energy of one pound of steam, of any qual- 

ity or condition; § 13 (/), (g) and. (j). 

K Table II, column 10. Internal or intrinsic energy of dry-sat- 

urated steam, above the state of water at 32 deg. fahr.; § 13 (/). 

k Internal energy of the liquid, differing by but a very little 

from the heat of the liquid or q; § 13 (/). 

I Table II, column 9. Inner latent heat, or the internal- 

energy portion of the whole heat r which is added during 
vaporization under a constant pressure p; § 13 (/). 

m Proportion of moisture in a mixture of water and steam, or 

the weight of liquid in one pound of the mixture; the " fraction 
of moisture " or " degree of wetness." 

N Table II, column 13. Total entropy of dry saturated steam, 

acquired in receiving the total heat H. It is the sum of the 
entropy of the liquid N q (called a, column 11) received with 
the water heat q, and of the entropy of vaporization N T (called 
b, column 12), received with the latent heat r. See § 13 (I). 

n Table VIII. Like h, n is used as a general symbol, especially 

for the total entropy of superheated steam above the state of 
water at 32 deg. See § 14 (6), page 91. 

Used for the entropy acquired by the steam in being super- 
heated at constant pressure, or in addition to the saturation 
value .V. See §13©. 



576 THE STEAM ENGINE AND TURBINE. 

P Pressure in pounds per square foot, as in APu, etc., above; 

see § 7 (d). 

p Table I, argument, Table II, column 1. Pressure of steam 

in pounds per square inch, absolute or above the zero of perfect 
vacuum; § 12 (a). 

ps Table III, column 5. The product of pressure p and specific 

steam volume s. 

pw Table III, column 4. The product of pressure p and specific 

water volume w. 

These quantities are useful in investigating the properties of 
steam and comparing it with a perfect gas — see § 12 (e). 
Also, they lead to APu and APw, noting that pu = ps — pw: 
see APu, etc., above. 

Q Heat of formation of the pound of steam, whether wet, dry- 

saturated, or superheated. This heat received from the fire is 
of the same nature as total heat H or h, but is measured above 
the state of water at the feed temperature U, instead of above 
32 deg. See § 13 (d). 

q Table II, column 6. Heat of the liquid, or heat required to 

raise one pound of water from 32 deg. to the vaporization tem- 
perature t; § 13 (6). 

R Constant or coefficient in the fundamental equation pv = RT; 

for steam (if a perfect gas) the value is 0.5956; see § 12 (e). 

M/p Table II, column 4. Ideal rate of expansion of superheated 

steam, or increment of volume per degree under the constant 
pressure p: to be used in calculating steam volume, as ex- 
plained in § 12 (i). 

r Table II, column 7. Latent heat or heat of vaporization, re- 

quired for the complete vaporization of one pound of water at 
pressure p and temperature t' h § 13 (c). 

s Table II, column 2. The specific volume of saturated steam 

(dry or completely vaporized), or the volume of one pound of 
steam in cubic feet; § 12 (c). 

s Later, in Chapter VI, § 27, etc., s is used as a symbol for de- 

grees of superheat or for (t — t s ) — this where there is no 
danger of confusing it with specific volume. 

s' Table II, column 3. The ideal specific volume of saturated 

steam, if it were a perfect gas under the law pv = RT: used in 
calculating the superheated volume v, as explained in § 12 (g) 
and (i). 

T Absolute temperature, t -f- 460 or, more exactly, t + 459.6; 

§ 12 (g). 



APPENDIX. 577 

t Table I, Table II, column 0, etc. Temperature of saturated 

steam, or of steam formation under the pressure p. Also used 
t s for temperature in general, as of superheated steam, with t B for 

the particular value at saturation; § 13 (h). 
u Volume increase during vaporization, under constant pressure 

p, from water volume w to steam volume s, in cubic feet per 

pound of steam; § 12 (d). 
v Specific volume in general, of steam wet or superheated; 

saturation volume s is a particular value of v. 
v Table VI. Specific volume of superheated steam; see § 12 

(i) for method of calculation, etc. 
v' Ideal specific volume of superheated steam, under the law 

pv = RT; used in getting the actual volume v, as explained in 

§ 12 ©. ^ 
w Table III, column 2. Specific water volume, or volume in 

cubic feet of one pound of water at temperature t and pressure 

V, § 12 (c). 
x Proportion of steam in a mixture of water and steam, or the 

weight of steam in one pound of the mixture; the " quality," 

" quality fraction," or " degree of dryness." 

C. Accuracy of the Steam Tables 

In regard to this mass of quantitative information, two questions 
arise. First, are the values essentially correct, or do they represent 
physical fact within the attainable degree of accuracy in determination? 
Second, are the successive numbers accurately spaced, so as to repre- 
sent smoothly and precisely the laws of variation of the quantities? 
For the second requirement; far greater numerical exactness is needed 
than for the first. 

The simplest property of saturated steam is the fundamental pres- 
sure-temperature relation, and this has been determined with a high 
degree of accuracy, even up to the critical temperature. Of the quan- 
tities used in thermodynamic calculations, the most important are 
specific volume and total heat. In these the range of experimental 
irregularity, or the departure of individual determinations from the 
mean curve, varies from 1 in 1000 to 1 in 400, on either side: this state- 
ment applies up to about 200 lb. pressure, while above that limit there 
are few direct data, but an increasing degree of extrapolation, inference, 
and uncertainty. 

The best that the combination and interpretation of physical data 
can do, in fixing a law of relation between total heat and pressure or 



578 



THE STEAM ENGINE AND TURBINE. 



Table I. Temperatures for Various Pressures. 

Argument, pressure in pounds per square inch above zero. 
Body of table, steam temperature in degrees fahrenheit. 



V 


0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 . 


0.8 


0.9 







35.03 


53.15 


64.50 


72.91 


79.66 


85.32 


90.19 


94.49 


98.34 


1 


101.84 


105.06 


108.02 


110.78 


113.36 


115.78 


118.07 


120.24 


122.30 


124.27 


2 


126.15 


127.95 


129.68 


131.34 


132.95 


134.50 


136.00. 


137.44 


138.84 


140.20 


3 


141.52 


142.80 


144.05 


145.27 


146.46 


147.61 


148.74 


149.84 


150.92 


151.97 


4 


153.00 


154.01 


155.00 


155.97 


156.92 


157.85 


158.77 


159.67 


160.55 


161.42 


5 


162.27 


163.11 


163.93 


164.74 


165.54 


166.32 


167.09 


167.85 


168.60 


169.34 


6 


170.07 


170.79 


171.50 


172.20 


172.89 


173.57 


174.24 


174.90 


175.56 


176.21 


7 


176.85 


177.48 


178.10 


178.72 


179.33 


179.93 


180.53 


181.12 


181.71 


182.29 


8 


182.86 


183.42 


183.98 


184.54 


185.09 


185.63 


186.17 


186.70 


187.23 


187.75 


9 


188.27 


188.78 


189.29 


189.80 


190.30 


190.79 


191.28 


191.77 


192.25 


192.73 







l 


2 


3 


4 


5 


6 


7 


8 


9 


10 


193.21 


197.75 


201.95 


205.87 


209.56 


213.03 


216.32 


219.43 


222.40 


225.24 


20 


227.96 


230.57 


233.08 


235.49 


237.82 


240.07 


242.25 


244.36 


246.41 


248.40 


30 


250.34 


252.22 


254.06 


255.84 


257.58 


259.29 


260.96 


262.58 


264.17 


265.73 


40 


267.26 


268.75 


270.22 


271.66 


273.07 


274.46 


275.82 


277.16 


278.47 


279.76 


50 


281.03 


282.28 


283.51 


284.72 


285.91 


287.09 


288.25 


289.39 


290.52 


291.63 


60 


292.73 


293.81 


294.88 


295.93 


296.97 


298.00 


299.02 


300.02 


301.01 


301.99 


70 


302.95 


303.91 


304.86 


305.79 


306.71 


307.63 


308.54 


309.43 


310.32 


311.20 


80 


312.07 


312.93 


313.78 


314.62 


315.46 


316.29 


317.11 


317.92 


318.72 


319.52 


90 


320.31 


321.10 


321.88 


322.65 


323.41 


324.17 


324.92 


325.66 


326.40 


327.13 


100 


327.86 


328.58 


329.30 


330.01 


330.71 


331.41 


332.11 


332.80 


333.48 


334.16 


110 


334.83 


335.50 


336.16 


336.82 


337.47 


338.12 


338.77 


339.41 


340.05 


340.68 


120 


341.31 


341.94 


342.56 


343.18 


343.79 


344.40 


345.00 


345.60 


346.20 


346.79 


130 


347.38 


347.97 


348.55 


349.13 


349.71 


350.28 


350.85 


351.42 


351.98 


352.54 


140 


353.10 


353.65 


354.20 


354.75 


355.29 


355.83 


356.37 


356.91 


357.44 


357.97 


150 


358.49 


359.02 


359.54 


360.06 


360.58 


361. Q? 


361.60 


362.11 


362.62 


363.12 


160 


363.62 


364.12 


364.61 


365.11 


365.60 


366.09 


366.57 


367.06 


367.54 


368.02 


170 


368.50 


368.97 


369.45 


369.92 


370.39 


370.85 


371.32 


371.78 


372.24 


372.70 


180 


373.15 


373.61 


374.06 


374.51 


374.96 


375.41 


375.85 


376.30 


376.74 


377.18 


190 


377.62 


378.05 


378.49 


378.92 


379.35 


379.78 


380.20 


380.63 


381.05 


381.47 


200 


381.89 


382.31 


382.73 


383.14 


383.56 


383.97 


384.38 


384.79 


385.20 


385.60 


210 


386.01 


386.41 


386.81 


387.21 


387.61 


388.01 


388.40 


388.80 


389.19 


389.58 







2 


4 


6 


8 





2 


4 


6 


8 


220 


389.97 


390.75 


391.52 


392.29 


393.05 


393.80 


394.55 


395.30 


396.04 


396.78 


240 


397.51 


398.23 


398.95 


399.67 


400.38 


401.09 


401.79 


402.49 


403.18 


403.87 


260 


404.56 


405.24 


405.92 


406.59 


407.26 


407.93 


408.59 


409.25 


409.90 


410.55 


280 


411.20 


411.84 


412.49 


413.13 


413.76 


414.39 


415.01 


415.64 


416.26 


416.87 


300 


417.49 


418.10 


418.71 


419.31 


419.91 


420.51 


421.11 


421.70 


422.29 


422.87 


320 


423.46 


424.04 


424.62 


425.19 


425.76 


426.33 


426.90 


427.46 


428.03 


428.59 


340 


429.14 


429.70 


430.25 


430.80 


431.35 


431.89 


432.43 


432.97 


433.51 


434.05 


360 


434.58 


435.11 


435.64 


436.17 


436.69 


437.21 


437.73 


438.25 


438.77 


439.28 


380 


439.79 


440.30 


440.81 


441.31 


441.82 


442.32 


442.82 


443.32 


443.81 


444.31 



APPENDIX. 579 

Table I. Temperatures for Various Pressures — Concluded. 



V 



50 


5 
55 


10 
60 


15 
65 


20 
70 


25 
75 


30 

80 


35 
85 


40 
90 


45 
05 


400 
450 
500 
550 


444.80 
456.51 
467.27 

477.22 


446.02 
457 . 63 
468.30 
478.18 


447.22 
458.73 
469.32 
479.13 


448.42 
459.83 
470.33 
480.07 


449.61 
460.92 
471.33 
481.01 


450.79 
462.00 
472.33 
481.94 


451.95 
463.07 
473.32 

482.86 


453.10 
464.13 
474.31 

483.78 


454.25 
465.18 
475.29 
484.69 


455.38 
466.23 
476.26 
485.60 







10 


20 


30 


40 


50 


60 


70 


80 


90 


600 
700 
800 
900 
1000 


486.50 
503.39 
518.48 
532.16 
544.69 


488.28 
504.97 
519.91 
533.46 


490.04 
506.53 
521.31 
534.75 


491.78 
508.08 
522.72 
536.03 


493.50 
509.61 
524.11 
537.29 


495.19 
511.13 
525.48 
538.55 


496.87 
512.63 
526.84 
539.80 


498.53 
514.11 
528.19 
541.04 


500.17 
515.58 
529.52 
542.26 


501.79 
517.04 
530.85 
543.48 



temperature for instance, is to locate the curve within a band from 1 
to 2 B.t.u. wide up to 200 lb. pressure, which runs to perhaps 5 or 
10 B.t.u. in width at 1000 lb. pressure. Closer delineation is a problem 
in graphical and mathematical method — the most useful scheme 
being to choose a simple mathematical formula which agrees fairly well 
with the trend of experiment, then plot to a large scale the differences 
between formula and observation, and trace a curve on this plane. 

As a statement of physical fact, a value of total heat carried to one 
decimal place is of the fullest degree of precision that our knowledge 
will justify, running one significant figure farther than what is surety 
known as to the absolute, local value of the quantity. In all calcula- 
tions where observations upon actual steam apparatus enter as data, 
the last figure or decimal place should be dropped from the numbers in 
Table I and in columns 1 and 6 to 13 of Table II. There are, however, 
certain calculations, as of the form of the ideal steam jet, where the 
result sought depends upon the relatively small difference between 
large total quantities, and it is to meet this case that the numbers in 
the tables are carried to five or six significant figures. 

In reading values for superheated steam from the diagrams in 
Tables VII and VIII, an error of 0.5 B.t.u. or its equivalent can easily 
be made. In comparison with a closeness of 0.1 B.t.u. for saturated 
steam, this about represents the difference in accuracy of physical 
data. With the original, full-size diagrams, an accuracy of 0.1 to 0.2 
B.t.u. was attainable; but there is an uncertainty in the relative spac- 
ing of the curves which is of at least this order of magnitude in the best 
part of the table, and which reaches perhaps one per cent (of the total 
heat) at the upper pressure limit of the diagrams. While close enough 
for all "practical" purposes, these diagrams do not give very satisfactory 
service in the calculations which require precisely expressed data. 

(Go to page 616) 






580 



THE STEAM ENGINE AND TURBINE. 



Table II. 



Principal Steam Table 






l 


2 


3 


4 


5 


6 


7 


Temp. deg. 
fahr. 


Press, lb. 
per sq. in. 


Sp. vol. 
cu. ft. 
per lb. 


Sp. vol. 
ideal. 


See definitions. 


Heat of 
liquid 
B.t.u. 


Latent heat 
B.t.u. 


t 


P 


s 


s' 


R/p 


/. 


2 


r 


32 


0.0886 


3304 


3305 


6.723 


1.310 


0.00 


1072.75 


33 


0.0922 


3180 


3181 


6.459 


1.301 


1.01 


1072.21 


34 


0.0960. 


3062 


3063 


6.206 


1.292 


2.01 


1071.67 


35 


0.0999 


2948 


2949 


5.963 


1.283 


3.02 


1071.13 


36 


0.1039 


2839 


2840 


5.731 


1.275 


4.02 


1070.60 


37 


0.1081 


2734 


2735 


5.508 


1.266 


5.03 


1070.06 


38 


0.1125 


2633 


2634 


5.294 


1.258 


6.03 


1069.52 


39 


0.1170 


2537 


2538 


5.090 


1.249 


7.04 


1068.98 


40 


0.1217 


2444 


2445 


4.895 


1.241 


8.04 


1068.44 


41 


0.1265 


2356 


2357 


4.708 


1.233 


9.0£ 


1067.90 


42 


0.1315 


2271 


2272 


4.529 


1.224 


10.05 


1067.36 


43 


0.1367 


2189 


2190 


4.358 


1.216 


11.05 


1066.82 


44 


0.1420 


2111 


2112 


4.194 


1.208 


12.05 


1066.28 


45 


0.1475 


2036 


2037 


4.038 


1.200 


13.05 


1065.74 


46 


0.1532 


1964 


1965 


3.888 


1.192 


14.05 


1065.20 


47 


0.1591 


1895 


1896 


3.744 


1.185 


15.05 


1064.66 


48 


0.1652 


1829 


1830 


3.605 


1.177 


16.05 


1064.12 


49 


0.1715 


1765 


1766 


3.473 


1.169 


17.05 


1063.57 


50 


0.1780 


1704 


1705 


3.346 


1.162 


18.05 


1063.03 


51 


0.1847 


1645 


1646 


3.224 


1.154 


19.05 


1062.49 


52 


0.1917 


1588 


1589 


3.107 


1.147 


20.05 


1061.95 


53 


0.1989 


1533 


1534 


2.994 


1.139 


21.05 


1061.41 


54 


0.2063 


1481 


1482 


2.886 


1.132 


22.05 


1060.86 


55 


0.2140 


1431 


1432 


2.783 


1.124 


23.05 


1060.32 


56 


0.2219 


1383 


1384 


2.684 


1.117 


24.05 


1059.78 


57 


0.2301 


1337 


1338 


2.589 


1.110 


25.05 


1059.24 


58 


0.2385 


1292 


1293 


2.498 


1.102 


26.05 


1058.69 


59 


0.2472 


1249 


1250 


2.410 


1.095 


27.04 


1058.15 


60 


0.2561 


1207 


1208 


2.326 


1.088 


28.04 


1057.61 


61 


0.2653 


1167 


1168 


2.245 


1.081 


29.04 


1057.06 


62 


0.2749 


1129 


1130 


2.167 


1.074 


30.04 


1056.52 


63 


0.2847 


1092 


1093 


2.092 


1.067 


31.03 


1055.98 . 


64 


0.2948 


1057 


1058 


2.020 


1.060 


32.03 


1055.43 


65 


0.3053 


1024 


1025 


1.951 


1.053 


33.03 


1054.89 


66 


0.3161 


990.9 


992.0 


1.8843 


1.046 


34.03 


1054.34 


67 


0.3272 


958.7 


959.8 


1.8205 


1.040 


35.02 


1053.80 


68 


0.3386 


927.7 


928.7 


1.7591 


1.033 


36.02 


1053.26 


69 


0.3504 


897.9 


898.9 


1.7000 


1.026 


37.02 


1052.71 


70 


0.3625 


869.2 


870.2 


1.6431 


1.020 


38.01 


1052.17 


71 


0.3750 


841.6 


842.5 


1.5883 


1.013 


39.01 


1051.63 


72 


0.3879 


815.0 


815.9 


1.5355 


1.007 


40.01 


1051.08 


73 


0.4012 


789.5 


790.4 


1.4847 


1.000 


41.00 


1050.54 


74 


0.4148 


765.0 


765.9 


1.4358 


0.994 


42.00 


1049.99 


75 


0.4289 


741.4 


742.4 


1.3887 


0.988 


43.00 


1049.44 



APPENDIX. 



581 



Principal Steam Table 



Table II. 



Total heat 
B.t.u. 

H 



1072.75 
1073.22 
1073.68 
1074.15 

1074.62 
1075.09 
1075.55 
1076.02 
1076.48 

1076.94 
1077.41 
1077.87 
1078.33 
1078.79 

1079.25 
1079.71 
1080.17 
1080.62 
1081.08 

1081.54 
1082.00 
1082.46 
1082.91 
1083.37 

1083.83 
1084.29 
1084.74 
1085.19 
1085.65 

1086.10 
1086.56 
1087.01 
1087.46 
1087.92 

1088.37 
1088.82 
1089.28 
1089.73 
1090.18 

1090.64 
1091.09 
1091.54 
1091.99 
1092.44 



Inner 
latent heat. 



10 

Inner total 
heat. 

K 



1018.58 
1017.93 
1017.28 
1016.63 

1015.99 
1015.34 
1014.69 
1014.04 
1013.39 

1012.74 
1012.09 
1011.44 
1010.79 
1010.14 

1009.49 
1008.84 
1008.19 
1007.54 
1006.89 

1006.24 
1005.59 
1004.94 
1004.28 
1003.63 

1002.98 
1002.33 
1001.68 
1001.03 
1000.38 

999.72 
999.07 
998.42 
997.77 
997.12 

996.46 
995.81 
995 . 16 
994.51 
993.86 

993.21 
992.55 
991.90 
991.24 
990.58 



1018.58 
1018.94 
1019.29 
1019.65 

1020.01 
1020.37 
1020.72 
1021.08 
1021.43 

1021.78 
1022.14 
1022.49 
1022.84 
1023.19 

1023.54 
1023.89 
1024.24 
1024.59 
1024.94 

1025.29 
1025.64 
1025.99 
1026.33 
1026.68 

1027.03 
1027.38 
1027.73 
1028.07 
1028.42 

1028.76 
1029.11 
1029.45 
1029.80 
1030.15 

1030.49 
1030.83 
1031.18 
1031.52 
1031.87 

1032.22 
1032.56 
1032.90 
1033.24 
1033.58 



n 



12 



Entropy of 
Liquid. Vapor'n. 



13 

Entropy- 
total. 

N 



0.00000 
0.00205 
0.00409 
0.00613 

0.00816 
0.01018 
0.01220 
0.01421 
0.01622 

0.01822 
0.02022 
0.02222 
0.02421 
0.02620 

0.02818 
0.03016 
0.03213 
0.03410 
0.03607 

0.03803 
0.03999 
0.04194 
0.04389 
0.04583 

0.04777 
0.04970 
0.05163 
0.05356 
0.05548 

0.05740 
0.05931 
0.06122 
0.06313 
0.06503 

0.06693 
0.06883 
0.07072 
0.07261 
0.07449 

0.07637 
0.07824 
0.08012 
0.08199 
0.08386 



2.18216 
2.17663 
2.17113 
2.16565 

2.16020 
2.15477 
2.14936 
2.14397 
2.13859 

2.13324 
2.12791 
2.12260 
2.11731 
2.11204 

2.10680 
2.10157 
2.09637 
2.09118 
2.08601 

2.08087 
2.07574 
2.07064 
2.06555 
2.06048 



2.18216 
2.17868 
2.17522 
2.17178 

2.16836 
2.16495 
2.16156 
2.15818 
2.15481 

2.15146 
2.14813 
2.14482 
2.14152 
2.13824 

2.13498 
2.13173 
2.12850 
2.12528 
2.12208 

2.11890 
2.11573 
2.11258 
2.10944 
2.10631 



Temp. deg. 
fahr. 



2.05543 


2.10320 


56 


2.05040 


2.10010 


57 


2.04539 


2.09702 


58 


2.04040 


2.09396 


59* 


2.03543 


2.09091 


60 


2.03048 


2.08788 


61 


2.02555 


2.08486 


62 


2.02063 


2.08185 


63 


2.01573 


2.07886 


64 


2.01085 


2.07588 


65 


2.00599 


2.07292 


66 


2.00115 


2.06998 


67 


1.99632 


2.06704 


68 


1.99151 


2.06412 


69 


1.98672 


2.06121 


70 


1.98195 


2.05832 


71 


1.97720 


2.05544 


72 


1.97246 


2.05258 


73 


1.96774 


2.04973 


74 


1.96304 


2.04690 


75 



32 
33 
34 
35 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 






582 



Table II. 



THE STEAM ENGINE AND TURBINE. 



Principal Steam Table 






1 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/v 


ft 


Q 


r 


75 


0.4289 


741.4 


742.4 


1.3887 


0.988 


43.00 


1049.44 


76 


0.4433 


718.6 


719.6 


1.3435 


0.981 


43.99 


1048.90 


77 


0.4582 


696.6 


697.6 


1.2999 


0.975 


44.99 


1048.35 


78 


0.4735 


675.3 


676.3 


1.2579 


0.969 


45.99 


1047.80 


79 


0.4893 


654.7 


655.7 


1.2173 


0.963 


46.98 


1047.25 


80 


0.5055 


634.8 


635.8 


1.1782 


0.957 


47.98 


1046.71 


81 


0.5222 


615.6 


616.6 


1.1405 


0.951 


48.97 


1046.16 


82 


0.5394 


597.0 


598.0 


1.1042 


0.945 


49.97 


1045.61 


83 


0.5570 


579.1 


580.0 


1.0693 


0.939 


50.97 


1045.06 


84 


0.5752 


561.8 


562.7 


1 .0355 


0.933 


51.96 


1044.52 


85 


0.5939 


545.2 


546.1 


1.0029 


0.927 


52.96 


1043.97 


86 


0.6132 


529.1 


530.0 


0.9714 


0.921 


53.95 


1043.42 


87 


0.6330 


513.5 


514.4 


0.9410 


0.916 


54.95 


1042.87 


88 


0.6533 


498.4 


499.3 


0.9116 


0.910 


55.95 


1042.32 


89 


0.6743 


483.8 


484.7 


0.8833 


0.904 


56.94 


1041.77 


90 


0.6958 


469.6 


470.5 


0.8560 


0.899 


57.94 


1041.22 


91 


0.7179 


455.9 


456.8 


0.8296 


0.893 


58.94 


1040.67 


92 


0.7406 


442.7 


443.6 


0.8041 


0.887 


59.93 


1040.12 


93 


0.7640 


429.9 


430.8 


0.7795 


0.882 


60.93 


1039.57 


94 


0.7880 


417.5 


418.4 


0.7558 


0.876 


61.92 


1039.02 


95 


0.8127 


405.5 


406.4 


0.7329 


0.871 


62.92 


1038.46 


96 


0.8380 


393.9 


394.8 


0.7108 


0.866 


63.92 


1037.91 


97 


0.8640 


382.7 


383.6 


0.6894 


0.860 


64.91 


1037.36 


98 


0.8907 


371.9 


372.8 


0.6687 


0.855 


65.91 


1036.80 


99 


0.9181 


361.5 


362.4 


0.6487 


0.850 


66.91 


1036.24 


100 


0.9462 


351.4 


352.2 


0.6294 


0.845 


67.90 


1035.69 


101 


0.9751 


341.6 


342.4 


0.6107 


0.839 


68.90 


1035 . 13 


102 


1.0047 


332.1 


332.9 


0.5927 


0.834 


69.90 


1034.57 


103 


1.0350 


322.9 


323.7 


0.5753 


0.829 


70.89 


1034.02 


104 


1.0662 


314.0 


314.8 


0.5585 


0.824 


71.89 


1033.47 


105 


1.0982 


305.4 


306.2 


0.5423 


0.819 


72.89 


1032.91 


106 


1.1310 


297.0 


297.8 


0.5266 


0.814 


73.88 


1032.36 


107 


1.1647 


288.9 


289.7 


0.5114 


0.809 


74.88 


1031.80 


108 


1 . 1992 


281.1 


281.9 


0.4967 


0.804 


75.88 


1031.24 


109 


1.2347 


273.5 


274.3 


0.4824 


0.799 


76.87 


1030.68 


110 


1.2711 


266.1 


266.9 


0.4686 


0.794 


77.87 


1030.12 


111 


1.3084 


258.9 


259.7 


0.4552 


0.789 


78.87 


1029.56 


112 


1.3466 


252.0 


252.8 


0.4422 


0.784 


79.86 


1029.00 


113 


1.3858 


245.3 


246.1 


0.4297 


0.779 


80.86 


1028.44 


114 


1.4260 


238.8 


239.6 


0.4176 


0.775 


81.86 


1027.88 


115 


1.4671 


232.5 


233.3 


0.4059 


0.770 


82.86 


1027.32 


116 


1.5093 


226.4 


227.2 


0.3946 


0.765 


83.85 


1026.76 


117 


1.5525 


220.5 


221.3 


0.3836 


0.761 


84.85 


1026.20 


118 


1.5968 


214.7 


215.5 


0.3730 


0.756 


85.85 


1025.63 


119 


1.6421 


209.1 


209.9 


0.3627 


0.751 


86.84 


1025.07 


120 


1.6886 


203.7 


204.5 


0.3527 


0.747 


87.84 


1024.50 


121 


1.7362 


198.4 


199.2 


0.3430 


0.742 


88.84 


1023.94 


122 


1.7849 


193.3 


194.0 


0.3336 


0.737 


89.84 


1023.37 


123 


1.8348 


188.3 


189.0 


0.3246 


0.733 


90.83 


1022.81 


124 


1.8859 


183.5 


184.2 


0.3158 


0.728 


91.83 


1022.24 


125 


1.9382 


178.8 


179.5 


0.3073 


0.724 


92.83 


1021 . 67 



APPENDIX. 



583 



Principal Steam Table 



Table II. 



8 


9 


10 


n 


12 


13 





H 


I 


K 


a 


b 


N 


t 


1092.44 


990.58 


1033.58 


0.08386 


1.96304 


2.04690 


75 


1092.89 


989.93 


1033.93 


0.08572 


1.95836 


2.04408 


76 


1093.34 


989.28 


1034.27 


0.08758 


1.95369 


2.04127 


77 


1093.79 


988.62 


1034.71 


0.08943 


1.94904 


2.03847 


78 - 


1094.23 


987.96 


1034.94 


0.09128 


1 . 94440 


2.03568 


79 


1094.68 


987.31 


1035.28 


0.09313 


1.93978 


2.03291 


80 


1095.13 


986.66 


1035.63 


0.09497 


1.93518 


2.03015 


81 


1095.58 


986.00 


1035.97 


0.09681 


1.93060 


2.02741 


82 


1096.03 


985.34 


1036.31 


0.09865 


1.92603 


2.02468 


83 


1096.48 


984.69 


1036.65 


0.10048 


1.92148 


2.02196 


84 


1096.93 


984.04 


1036.99 


0.10231 


1.91694 


2.01925 


85 


1097.37 


983.38 


1037.33 


0.10414 


1.91242 


2.01656 


86 


1097.82 


982.72 


1037.67 


0.10596 


1.90792 


2.01388 


87 


1098.27 


982.06 


1038.01 


0.10778 


1.90343 


2.01121 


88 


1098.71 


981.41 


1038.35 


. 10960 


1.89896 


2.00856 


89 


1099.16 


980.75 


1038.69 


0.11142 


1.89459 


2.00592 


90 


1099.61 


980.09 


1039.03 


0.11323 


1.89006 


2.00329 


91 


1100.05 


979.43 


1039.37 


0.11504 


1.88563 


2.00067 


92 


1100.50 


978.77 


1039.71 


0.11684 


1.88122 


1.99806 


93. 


1100.94 


978.11 


1040.04 


0.11864 


1.87683 


1.99547 . 


94 


1101.38 


977.45 


1040.37 


0.12044 


1.87245 


1.99289 


95 


1101.83 


976.89 


1040.71 


0.12224 


1.86809 


1.99033 


96 


1102.27 


976.13 


1041.05 


0.12403 


1.86374 


1.98777 


97 


1102.71 


975.47 


1041.38 


0.12582 


1.85940 


1.98522 


98 


1103.15 


974.81 


1041.71 


0.12761 


1.85508 


1.98269 


99 


1103.59 


974.15 


1042.05 


0.12939 


1.85077 


1.98016 


100 


1104.03 


973.48 


1042.38 


0.13177 


1.84648 


1 . 97765 


101 


1104.47 


972.82 


1042.71 


0.13295 


1.84220 


1.97515 


102 


1104.91 


972.16 


1043.05 


0.13472 


1.83794 


1.97266 


103 


1105.36 


971.50 


1043.39 


0.13649 


1.83369 


1.97018 


104 


1105.80 


970.84 


1043.72 


0.13826 


1.82946 


1.96772 


105 


1106.24 


970.18 


1044.06 


0.14002 


1.82524 


1.96526 


106 


1106.68 


969.52 


1044.39 


0.14178 


1.82104 


1 . 96282 


107 


1107.12 


968.85 


1044.72 


0.14354 


1.81685 


1.96039 


108 


1107.55 


968.18 


1045.05 


0.14529 


1.81267 


1.95796 


109 


1107.99 


967.52 


1045.39 


0.14704 


1.80850 


1.95554 


110 


1108.43 


966.85 


1045.72 


0.14879 


1.80435 


1.95314 


111 


1108.86 


966.18 


1046.04 


0.15053 


1.80021 


1.95074 


112 


1109.30 


965.52 


1046.38 


0.15227 


1.79609 


1.94836 


113 


1109.74 


964.85 


1046.71 


0.15401 


1.79198 


1.94599 


114 


1110.18 


964.19 


1047.04 


0.15575 


1.78789 


1.94364 


115 


1110.61 


963.53 


1047.37 


0.15748 


1.78381 


1.94129 


116 


1111.05 


962.86 


1047.70 


0.15921 


1.77974 


1.93895 


117 


1111.48 


962.19 


1048.03 


0.16094 


1.77568 


1.93662 


118 


1111.91 


961.52 


1048.36 


. 16267 


1.77164 


1.93431 


119 


1112.34 


960.85 


1048.68 


0.16439 


1.76761 


1.93200 


120 


1112.78 


960.18 


1049.01 


0.16611 


1.76359 


1.92970 


121 


1113.21 


959.51 


1049.34 


0.16783 


1 . 75959 


1.92742 


122 


1113.64 


958.94 


1049.66 


0.16954 


1.75560 


1.92514 


123 


1114.07 


958.17 


1049.99 


0.17125 


1.75162 


1.92287 


124 


1114.50 


957.49 


1050.31 


0.17296 


1.74765 


1.92061 


125 



584 



THE STEAM ENGINE AND TURBINE. 



Table II. . 



Principal Steam Table 






l 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/P 


A 


Q 


r 


125 


1.938 


178.82 


179.55 


0.3073 


0.724 


92.83 


1021 . 67 


126 


1.992 


174.33 


175.06 


0.2990 


0.719 


93.83 


1021.10 


127 


2.047 


169.96 


170.68 


0.2910 


0.715 


94.82 


1020.54 


128 


2.103 


165.71 


166.53 


0.2832 


0.711 


95.82 


1019.97 


129 


2.160 


161.58 


162.30 


0.2757 


0.706 


96.82 


1019.40 


130 


2.219 


157.57 


158.28 


0.2684 


0.702 


97.82 


1018.83 


131 


2.279 


153.67 


154.38 


0.2613 


0.698 


98.82 


1018.26 


132 


2.341 


149.88 


150.58 


0.2544 


0.693 


99.81 


1017.69 


133 


2.403 


146.19 


146.89 


0.2477 


0.689 


100.81 


1017.12 


134 


2.468 


142.60 


143.29 


0.2413 


0.685 


101.81 


1016.55 


135 


2.533 


139.12 


139.80 


0.2351 


0.681 


102.81 


1015.97 


136 


2.600 


135.73 


136.41 


0.2291 


0.676 


103.81 


1015.40 


137 


2.669 


132.43 


133.11 


0.2232 


0.672 


104.81 


1014.82 


138 


2.740 


129.23 


129.90 


0.2175 


0.668 


105.80 


1014.25 


139 


2.812 


126.13 


126.80 


0.2119 


0.664 


106.80 


1013.68 


140 


2.885 


123rl2 


123.78 


0.20644 


0.660 


107.80 


1013.10 


141 


2.960 


120.19 


120.85 


0.20122 


0.656 


108.80 


1012.52 


142 


3.037 


117.34 


118.00 


0.19614 


0.652 


109.80 


1011.95 


143 


3.116 


114.56 


115.22 


0.19120 


0.648 


110.80 


1011.37 


144 


3.196 


111.86 


112.51 


0.18640 


.0.644 


111.80 


1010.79 


145 


3.278 


109.23 


109.87 


0.18174 


0.640 


112.80 


1010.21 


146 


3.361 


106.67 


107.31 


0.17621 


0.636 


113.80 


1009.63 


147 


3.447 


104.18 


104.82 


0.17281 


0.632 


114.80 


1009.05 


148 


3.534 


101.76 


102.40 


0.16853 


0.628 


115.79 


1008.47 


149 


3.623 


99.41 


100.04 


0.16437 


0.624 


116.79 


1007.89 


150 


3.715 


97.13 


97.76 


0.16033 


0.620 


117.79 


1007.31 


151 


3.808 


94.91 


95.53 


0.15641 


0.616 


118.79 


1006.73 


152 


3.903 


92.74 


93.36 


0.15260 


0.613 


119.79 


1006.15 


153 


4.000 


90.63 


91.21 


0.14890 


0.609 


120.79 


1005.56 


154 


4.099 


88.57 


89.18 


0.14531 


0.605 


121.79 


1004.98 


155 


4.200 


86.57 


87.18 


0.14182 


0.601 


122.79 


1004.39 


156 


4.303 


84.62 


85.22 


0.13842 


0.598 


123.79 


1003.80 


157 


4.408 


82.72 


83.32 


0.13511 


0.594 


124.79 


1003.22 


158 


4.516 


80.87 


81.46 


0.13189 


0.590 


125.79 


1002.63 


159 


4.625 


79.07 


79.66 


0.12876 


0.587 


126.79 


1002.04 


160 


4.737 


77.32 


77.90 


0.12572 


0.583 


127.79 


1001.45 


161 


4.852 


75.61 


76.19 


0.12276 


0.580 


128.80 


1000.86 


162 


4.968 


73.94 


74.52 


0.11988 


0.576 


129.80 


1000.27 


163 


5.087 


72.32 


72.89 


0.11708 


0.573 


130.80 


999.68 


164 


5.208 


70.74 


71.31 


0.11435 


0.569 


131.80 


999.09 


. 165 


5.332 


69.20 


69.77 


0.11170 


0.566 


132.80 


998.49 


166 


5.459 


67.70 


68.27 


0.10911 


0.563 


133.80 


997.90 


167 


5.588 


66.24 


66.80 


0.10659 


0.559 


134.80 


997.31 


168 


5.719 


64.81 


65.37 


0.10414 


0.556 


135.80 


996.71 


169 


5.853 


63.42 


63.98 


0.10175 


0.553 


136.80 


996.12 


170 


5.990 


62.06 


62.62 


0.09943 


0.549 


137.80 


995.52 


171 


6.129 


60.73 


61.29 


0.09717 


0.546 


138.81 


994.92 


172 


6.271 


59.44 


59.99 


0.09497 


0.543 


139.81 


994.33 


173 


6.416 


58.18 


58.73 


0.09283 


0.540 


140.81 


993.73 


174 


6.564 


56.95 


57.49 


0.09074 


0.536 


141.81 


993 . 13 


175 


6.714 


55.75 


56.29 


0.08871 


0.533 


142.82 


992.53 



APPENDIX. 



585 



Principal Steam Table 



Table II. 






8 


9 


10 


11 


12 


13 





H 


I 


K 


a 


b 


JV j 


t 


1114.50 


957.49 


1050.31 


0.17296 


1.74765 


1.92061 


125 


1114.93 


956.82 


1050.64 


0.17467 


1.74370 


1.91837 


126 


1115.36 


956.15 


1050.96 


0.17637 


1.73976 


1.91613 


127 . 


1115.79 


955.48 


1051.29 


0.17807 


1.73583 


1.91390 


128 


1116.22 


954.80 


1051.61 


0.17977 


1.73191 


1.91168 


129 


1116.65 


954.13 


1051.94 


0.18146 


1.72801 


1.90947 


130 


1117.08 


953.45 


1052.26 


0.18315 


1.72412 


1.90727 


131 


1117.50 


952.78 


1052.58 


0.18484 


1.72024 


1.90508 


132 


1117.93 


952.10 


1052.90 


0.18653 


1.71637 


1.90290 


133 


1118.36 


951.43 


1053.23 


0.18821 


1.71251 


1.90072 


134 


1118.78 


950.75 


1053.55 


0.18989 


1.70867 


1.89856 


135 


1119.21 


950.07 


1053.87 


0.19157 


1.70484 


1.89641 


136 


1119.63 


949.39 


1054.19 


0.19324 


1.70102 


1.89426 


137 


1120.05 


948.71 


1054.51 


0.19491 


1 . 69721 


1.89212 


138 


1120.48 


948.04 


1054.83 


0.19658 


1 . 69341 


1.88999 


139 


1120.90 


947.36 


1055.15 


0.19825 


1.68963 


1.88788 


140 


1121.32 


946.68 


1055.47 


0.19991 


1.68586 


1.88577 


141 


1121.75 


946.00 


1055.79 


0.20157 


1.68210 


1.88367 


142 


1122.17 


945.32 


1056.11 


0.20323 


1.67835 


1.88158 


143 


1122.59 


944.64 


1056.43 


0.20489 


1.67461 


1.87950 


144 


1123.01 


943.96 


1056.75 


0.20654 


1 . 67088 


1.87742 


145 


1123.43 


943.27 


1057.06 


0.20819 


1.66716 


1.87535 


146 


1123.85 


942.59 


1057.38 


0.20984 


1.66345 


1.87329 


147 


1124.26 


941.91 


1057.69 


0.21149 


1.65976 


1.87125 


148 


1124.68 


941.23 


1058.01 


0.21314 


1.65608 


1.86922 


149 


1125.10 


940.55 


1058.33 


0.21478 


1.65241 


1.86719 


150 


1125.52 


939.86 


1058.64 


0.21642 


1.64875 


1.86517 


151 


1125.94 


939.18 


1058.96 


0.21806 


1.64510 


1.86316 


152 


1126.35 


938.49 


1059.27 


0.21969 


1.64146 


1.86115 


153 


1126.77 


937.81 


1059.59 


0.22132' 


1.63783 


1.85915 


154 


1127.18 


937.12 


1059.90 


0.22295 


1 . 63421 


1.85716 


155 


1127.59 


936.43 


1060.21 


0.22458 


1 . 63060 


1.85518 


156 


1128.01 


935.74 


1060.52 


0.22620 


1.6.2700 


1.85320 


157 


1128.42 


935.05 


1060.83 


0.22782 


1.62341 


1.85123 


158 


1128.83 


934.36 


1061.14 


0.22944 


1.61984 


1.84928 


159 


1129.24 


933.67 


1061.45 


0.23105 


1.61628 


1.84733 


160 


1129.66 


932.98 


1061.77 


0.23266 


1.61273 


1.84539 


161 


1130.07 


932.30 


1062.08 


0.23427 


1.60918 


1.84345 


162 


1130.48 


931.61 


1062.39 


0.23588 


1.60565 


1.84153 


163 


1130.89 


930.92 


1062.70 


0.23749 


1.60212 


1.83961 


164 


1131.29 


930.22 


1063.00 


0.23909 


1.59861 


1.83770 


165 


1131.70 


929.53 


1063.31 


0.24069 


1.59511 


1.83580 


166 


1132.11 


928.84 


1063.62 


0.24229 


1.59161 


1.83390 


167 


1132.51 


928.14 


1063.92 


0.24389 


1.58813 


1.83202 


168 


1132.92 


927.45 


1064.23 


0.24549 


1.58465 


1.83014 


169 


1133.32 


926.75 


1064.53 


0.24708 


1.58119 


1.82827 


170 


1133.73 


926.05 


1064.84 


0.24867 


1.57774 


1.82641 


171 


1134.14 


925.36 


1065.15 


0.25026 


1.57430 


1.82456 


172 


1134.54 


924.66 


1065.45 


0.25184 


1.57087 


1.82271 


173 


1134.94 


923.96 


1065.75 


0.25342 


1.56744 


1.82086 


174 


1135.35 


923.27 


1066.07 


0.25500 


1.56402 


1 . 81902 


175 



586 



THE STEAM ENGINE AND TURBINE. 



Table II. 



Principal Steam Table 






1 


2 


3 


4 


5 


6 


7 


t 


p 


s 


s' 


R/p 


ft 


Q 


r 


175 


6.714 


55.75 


56.29 


0.08871 


0.533 


142.82 


992.53 


176 


6.867 


54.58' 


55.12 


0.08673 


0.530 


143.82 


991.93 


177 


7.024 


53.44 


53.97 


0.08480 


0.527 


144.82 


991.33 


178 


7.183 


52.33 


52.86 


0.08292 


0.523 


145.82 


990.73 


179 


7.345 


51.25 


51.77 


0.08109 


0.520 


146.83 


990.12 


180 


7.511 


50.20 


50.72 


0.07930 


0.517 


147.83 


989.51 


181 


7.679 


49.17 


49.69 


0.07756 


0.514 


148.83 


988.91 


182 


7.850 


48.17 


48.68 


0.07587 


0.511 


149.84 


988.30 


183 


8.025 


47.19 


47.70 


0.07422 


0.508 


150.84 


987.70 


184 


8.203 


46.23 


46.74 


0.07261 


0.504 


151.84 


987.09 


185 


8.384 


45.29 


45.80 


0.07104 


0.501 


152.85 


986.48 


186 


8.568 


44.38 


44.88 


0.06951 


0.498 


153.85 


985.87 


187 


8.756 


43.49 


43.99 


0.06802 


0.495 


154.85 


985.26 


188 


8.947 


42.62 


43.12 


0.06657 


0.492 


155.86 


984.65 


189 


9.142 


41.77 


42.26 


0.06515 


0.489 


156.86 


984.04 


190 


9.340 


40.93 


41.42 


0.06377 


0.486 


157.87 


983.42 


191 


9.542 


40.12 


40.61 


0.06242 


0.483 


158.87 


982.81 


192 


9.747 


39.33 


39.82 


0.06110 


0.480 


159.88 


982.19 


193 


9.956 


38.56 


39.04 


0.05982 


0.477 


160.88 


981.58 


194 


10.169 


37.80 


38.28 


0.05857 


0.474 


161.88 


980.97 


195 


10.385 


37.06 


37.54 


0.05735 


0.472 


162.89 


980.35 


196 


10.606 


36.34 


36.82 


0.05616 


0.469 


163.89 


979.74 


197 


10.830 


35.64 


36.11 


0.05500 


0.466 


164.90 


979 . 12 


198 


11.058 


34.95 


35.42 


0.05386 


0.463 


165.90 


978.50 


199 


11.291 


34.28 


34.75 


0.05275 


0.460 


166.91 


977.88 


200 


11.527 


33.62 


34.09 


0.05167 


0.458 


167.92 


977.25 


201 


11.767 


32.98 


33.44 


0.05061 


0.455 


168.92 


976.63 


202 


12.012 


32.35 


32.81 


0.04958 


0.452 


169.93 


976.00 


203 


12.261 


31.74 


32.20 


0.04857 


0.450 


170.94 


975.37 


204 


12.514 


31.14 


31.59 


0.04759 


0.447 


171.94 


974.75 


205 


12.771 


30.55 


31.00 


0.04663 


0.444 


172.95 


974.12 


206 


13.033 


29.97 


30.42 


0.04569 


0.442 


173.95 


973.50 


207 


13.299 


29.41 


29.86 


0.04478 


0.439 


174.96 


972.87 


208 


13.569 


28.86 


29.30 


0.04389 


0.437 


175.97 


972.24 


209 


13.844 


28.32 


28.76 


0.04302 


0.434 


176.97 


971.61 


210 


14.124 


27.80 


28.24 


0.04217 


0.432 


177.98 


970.97 


211 


14.408 


27.28 


27.72 


0.04134 


0.429 


178.99 


970.34 


212 


14.697 


26.78 


27.22 


0.04052 


0.427 


180.00 


969.70 


213 


14.991 


26.29 


26.72 


0.03973 


0.424 


181.01 


969.06 


214 


15.290 


25.81 


26.24 


0.03895 


0.422 


182.01 


968.43 


215 


15.593 


25.34 


25.77 


0.03819 


0.420 


183.02 


967.79 


216 


15 901 


24.88 


25.31 


0.03745 


0.417 


184.03 


967.15 


217 


16.215 


24.43 


24.85 


0.03673 


0.415 


185.04 


966.51 


218 


16.534 


23.99 


24.41 


0.03602 


0.413 


186.05 


965.86 


219 


16.858 


23.56 


23.98 


0.03533 


0.410 


187.06 


965.22 


220 


17.187 


23.13 


23.55 


0.03465 


0.408 


188.07 


964.58 


221 


17.522 


22.72 


23.14 


0.03399 


0.406 


189.08 


963.93 


222 


17.862 


22.32 


22.73 


0.03334 


0.403 


190.09 


963.29 


223 


18.207 


21.92 


22.33 


0.03271 


0.401 


191.10 


962.64 


224 


18.558 


21.53 


21.94 


0.03209 


0.399 


192.11 


961.99 


225 


18.915 


21.15 


21.56 


0.03148 


0.396 


193.12 


961.35 






APPENDIX. 



587 



Principal Steam Table 



Table II. 



8 


9 


10 


11 


12 


13 





H 


, I 


K 


a 


b 


N 


t 


1135.35 


923.27 


1066.07 


0.25500 


1.56402 


1.81902 


175 


1135.75 


922.57 


1066.37 


0.25658 


1.56061 


1.81719 


176 


1136.15 


921.87 


1066.67 


0.25816 


1.55722 


1.81538 


177 


1136.55 


921.17 


1066.97 


0.25973 


1.55383 


1.81356 


178 


1136.95 


920.46 


1067.27 


0.26130 


1.55045 


1.81175 


179 


1137.34 


919.76 


1067.57 


0.26287 


1.54708 


1.80995 


180 


1137.74 


919.06 


1067.87 


0.26444 


1.54372 


1.80816 


181 


1138.14 


918.35 


1068.17 


0.26600 


1.54037 


1.80637 


182 


1138.54 


917.65 


1068.47 


0.26756 


1.53702 


1.80458 


183 


1138.93 


916.94 


1068.76 


0.26912 


1.53369 


1.80281 


184 


1139.33 


916.24 


1069.06 


0.27068 


1.53037 


1.80105 


185 


1139.72 


915.53 


1069.36 


0.27224 


1.52706 


1.79930 


186 


1140.11 


914.82 


1069.65 


0.27379 


1.52376 


1.79755 


187 


1140.51 


914.12 


1069.95 


0.27534 


1.52046 


1.79580 


188 


1140.90 


913.41 


1070.24 


0.27689 


1.51717 


1.79406 


189 


1141.29 


912.70 


1070.54 


0.27844 


1.51389 


1.79233 


190 


1141.68* 


911.99 


1070.83 


0.27999 


1.51062 


1.79061 


191 


1142.07 


911.27 


1071.12 


0.28153 


1.50736 


1.78889 


192 


1142.46 


9m-. 56 


1071.41 


0.28307 


1.50411 


1.78718 


193 


1142.85 


909.86 


1071.71 


0.28461 


1.50086 


1.78547 


194 


1143.24 


909 . 14 


1072.00 


0.28615 


1.49763 


1.78378 


195 


1143.63 


908.43 


1072.29 


0.28768 


1.49440 


1.78208 


196 


1144.01 


907.72 


1072.58 


0.28921 


1.49118 


1.78039 


197 


1144.40 


907.00 


1072.87 


0.29074 


1.48797 


1.77871 


198 


1144.78 


906.29 


1073.16 


0.29227 


1.48477 


1.77704 


199 


1145.17 


905.57 


1073.45 


0.29380 


1.48157 


1.77537 


200 


1145.55 


904.85 


1073.74 


0.29532 


1.47838 


1.77370 


201 


1145.93 


904.13 


1074.02 


0.29684 


1.47520 


1.77204 


202 


1146.31 


903.41 


1074.31 


0.29836 


1.47203 


1.77039 


203 


1146.69 


902.69 


1074.59 


0.29988 


1.46887 


1.76875 


204 


1147.07 


901.97 


1074.88 


0.30140 


1.46572 


1.76712 


205 


1147.45 


901.25 


1075.16 


0.30292 


1.46258 


1.76550 


206 


1147.83 


900.53 


1075.45 


0.30443 


1.45944 


1.76387 


207 


1148.21 


899.81 


1075.73 


0.30594 


1.45631 


1.76225 


' 208 


1148.58 


899.08 


1076.01 


0.30745 


1.45319 


1.76064 


209 


1148.95 


898.25 


1076.29 


0.30896 


1.45008 


1.75904 


210 


1149.33 


897.63 


1076.57 


0.31047 


1.44697 


1.75744 


211 


1149.70 


896.90 


1076.85 


0.31198 


1.44387 


1.75585 


212 


1150.07 


896.17 


1077.13 


0.31348 


1.44078 


1.75426 


213 


1150.44 


895.44 


1077.40 


0.31498 


1.43770 


1.75268 


214 


1150.81 


894.71 


1077.68 


0.31648 


1.43462 


1.75110 


215 


1151.18 


893.98 


1077.96 


0.31797 


1.43155 


1.74952 


216 


1151.55 


893.25 


1078.24 


0.31946 


1.42849 


1.74795 


217 


1151.91 


892.51 


1078.51 


0.32095 


1.42544 


1.74639 


218 


1152.28 


891.77 


1078.78 


0.32244 


1.42239 


1.74483 


219 


1152.65 


891.04 


1079.06 


0.32392 


1.41935 


1.74327 


220 


1153.01 


890.30 


1079.33 


0.32540 


1.41632 


1.74172 


221 


1153.38 


889.57 


1079.60 


0.32688 


1.41329 


1.74017 


222 


1153.74 


888.83 


1079.87 


0.32836 


1.41027 


1.73863 


223 


1154.10 


888.09 


1080.14 


0.32984 


1.40726 


1.73710 


224 


1154.47 


887.36 


1080.42 


0.33132 


1.40426 


1.73558 


225 



588 



THE STEAM ENGINE AND TURBINE. 



Table II. 



Principal Steam Table 






1 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s" 


R/p 


ft 


Q 


r 


225 


18.92 


21.152 


21.559 


.03148 


0.396 


193.12 


961.35 


226 


19.28 


20.781 


21.185 


.03088 


0.394 


194.13 


960.70 


227 


19.64 


20.417 


20.819 


.03031 


0.392 


195 . 14 


960.05 


228 


20.01 


20.061 


20.461 


.02975 


0.390 


196.15 


959.40 


229 


20.39 


19.712 


20.109 


.02920 


0.388 


197.16 


958.75 


230 


20.78 


19.370 


19.766 


.02867 


0.385 


198.17 


958.09 


231 


21.17 


19.035 


19.428 


.02814 


0.383 


199.18 


957.44 


232 


21.57 


18.707 


19.098 


.02762 


0.381 


200.19 


956.78 


233 


21.97 


18.386 


18.776 


.02711 


0.379 


201.20 


956.13 


234 


22.38 


18.071 


18.459 


.02661 


0.377 


202.22 


955.47 


235 


22.80 


17.763 


18.149 


.02612 


0.375 


203 23 


954.81 


236 


23.22 


17.461 


17.846 


.02565 


0.372 


204.24 


954.15 


237 


23.65 


17.165 


17.548 


.02519 


0.370 


205.25 


953.48 


238 


24.08 


16.875 


17.256 


.02474 


0.368 


206.27 


952.82 


239 


24.52 


16.591 


16.971 


.02430 


0.366 


207.28 


952.16 


240 


24.97 


16.312 


16.690 


.02386 


0.364 


208.29 


951.49 


241 


25.42 


16.039 


16.415 


.02343 


0.362 


209.31 


950.82 


242 


25.88 


15.771 


16.145 


.02301 


0.360 


210.32 


950 . 16 


243 


26.35 


15.509 


15.881 


.02260 


0.358 


211.33 


949.49 


244 


26.83 


15.252 


15.623 


.02220 


0.356 


212.35 


948.82 


245 


27.31 


15.000 


15.369 


.02181 


0.354 


213.36 


948.14 


246 


27.80 


14.753 


15.020 


.02143 


0.352 


214.38 


947.47 


247 


28.30 


14.511 


14.876 


.02105 


0.351 


215.39 


946.80 


248 


28.80 


14.273 


14.637 


.02068 


0.349 


216.40 


946.12 


249 


29.31 


14.040 


14.402 


.02032 


0.347 


217.42 


945.45 


250 


29.82 


13.812 


14.172 


.019971 


0.345 


218.43 


944.77 


251 


30.35 


13.588 


13.947 


.019625 


0.343 


219.45 


944.09 


252 


30.88 


13.368 


13.725 


.019286 


0.341 


220.47 


943.41 


253 


31.42 


13.153 


13.508 


018954 


0.340 


221.48 


942.73 


254 


31.97 


12.942 


13.296 


.018629 


0.338 


222.50 


942.04 


255 


32.52 


12.735 


13.087 


.018311 


0.336 


223.51 


941.36 


256 


33.09 


12.532 


12.882 


.017999 


0.334 


224.53 


940.68 


257 


33.66 


12.333 


12.681 


.017693 


0.332 


225.55 


939.99 


258 ■ 


34.24 


12.137 


12.484 


.017394 


0.330 


226.56 


939.31 


259 


34.83 


11.945 


12.291 


.017101 


0.329 


227.58 


938.62 


260 


35.42 


11.756 


12.100 


.016814 


0.3271 


228.59 


937.93 


261 


36.03 


11.571 


11.914 


.016532 


0.3254 


229.61 


937.24 


262 


36.64 


11.390 


11.731 


.016255 


0.3237 


230.63 


936.54 


263 


37.26 


11.212 


11.552 


.015984 


0.3220 


231.65 


935.85 


264 


37.89 


11.037 


11.375 


.015718 


0.3203 


232.67 


935.15 


265 


38.53 


10.865 


11.202 


.015457 


0.3186 


233.69 


934.46 


266 


39.18 


10.697 


11.032 


.015202 


0.3169 


234.70 


933.76 


267 


39.83 


10.532 


10.866 


.014952 


0.3152 


235.72 


933.06 


268 


40.49 


10.370 


10.702 


.014707 


0.3136 


236.74 


932.37 


269 


41.17 


10.211 


10.542 


.014467 


0.3119 


237.76 


931.67 


270 


41.85 


10.055 


10.385 


.014232 


0.3103 


t 238.78 


930.97 


271 


42.54 


9.902 


10.230 


.014001 


0.3087 


239.80 


930.27 


272 


43.24 


9.751 


10.077 


.013774 


0.3071 


240.82 


929.56 


273 


43.95 


9.603 


9.928 


.013551 


0.3055 


241.84 


928.86 


274 


44.67 


9.458 


9.781 


.013333 


0.3039 


242.86 


928.15 


275 


45.40 


9.315 


9.637 


.013119 


0.3023 


243.88 


927.44 



APPENDIX. 



589 





- 


Principa 


l Steam 


Table 


Table II. 


8 


9 


10 


u 


12 


13 





H 


I 


K 


a 


b 


N 


t 


1154.47 


887.36 


1080.42 


0.33132 


1.40426 


1.73558 


225 


1154.83 


886.62 


1080.69 


0.33280 


1.40127 


1.73407 


226 


1155.19 


885.88 


1080.96 


0.33427 


1.39828 


1.73255 


227 


1155.55 


885.14 


1081 . 32 


0.33574 


1.39530 


1.73104 


228' 


1155.91 


884.40 


1081.50 


0.33721 


1.39232 


1.72953 


229 


1156.26 


883.66 


1081.76 


0.33868 


1.38935 


1.72803 


230 


1156.62 


882.92 


1082.03 


0.34015 


1.38639 


1.72654 


231 


1156.97 


882.17 


1082.29 


0.34161 


1.38344 


1.72505 


232 


1157.33 


881.43 


1082.56 


0.34307 


1.38049 


1.72356 


233 


1157.69 


880.69 


1082.83 


0.34453 


1.37755 


1.72208 


234 


1158.04 


879.94 


1083.10 


0.34599 


1.37462 


1.72061 


235 


1158.39 


879.19 


1083.36 


0.34745 


1.37169 


1.71914 


236 


1158.74 


878.44 


1083.62 


0.34891 


1.36877 


1.71768 


237 


1159.09 


877.69 


1083.88 


0.35036 


1.36586 


1.71622 


238 


1159.44 


876.94 


1084.14 


0.35181 


1.36295 


1.71476 


239 


1159.78 


876.19 


1084.40 


0.35326 


1.36005 


1.71331 


240 


1160.13 


875.43 


1084.66 


0.35471 


1.35716 


1.71187 


241 


1160.48 


874.68 


1084.92 


0.35616 


1.35427 


1.71043 


242 


1160.82 


873.93 


1085.18 


0.35760 


1.35139 


1.70899 


243 


1161.17 


873.17 


1085.44 


0.35904 


1.34852 


1.70756 


244 


1161.51 


872.41 


1085.69 


0.36048 


1.34565 


1.70613 


245 


1161.85 


871.66 


1085.95 


0.36192 


1.34279 


1.70471 


246 


1162.19 


870.90 


1086.20 


0.36336 


1.33994 


1.70330 


247 


1162.52 


870.14 


1086.45 


0.36480 


1.33709 


1.70189 


248 


1162.86 


869.38 


1086.70 


0.36623 


1.33425 


1.70048 


249 


1163.20 


868.62 


1086.96 


0.36766 


1.33141 


1.69907 


250 


1163.54 


867.86 


1087.21 


0.36909 


1.32858 


1.69767 . 


251 


1163.88 


867.10 


1087.46 


0.37052 


1.32576 


1.69628 


252 


1164.21 


866.33 


1087.71 


0.37195 


1.32294 


1.69489 


253 


1164.54 


865.56 


1087.96 


0.37337 


1.32013 


1.69350 


254 


1164.87 


864.80 


1088.21 


0.37479 


1.31733 


1.69212 


255 


1165.21 


864.04 


1088.46 


0.37621 


1.31453 


1.69074 


256 


1165.54 


863.27 


1088.71 


0.37763 


1.31174 


1.68937 


257 


1165.87 


862.51 


1088.96 


0.37905 


1.30895 


1.68800 


258 


1166.20 


861.74 


1089.21 


0.38047 


1.30617 


1.68664 


259 


1166.52 


860.97 


1089.45 


0.38188 


1.30340 


1.68528 


260 


1166.85 


860.20 


1089.70 


0.38329 


1.30063 


1.68392 


261 


1167.17 


859.42 


1089.94 


0.38470 


1.29787 


1 . 68257 


262 


1167.50 


858.65 


1090.18 


0.38611 


1.29512 


1.68123 


263 


1167.82 


857.87 


1090.42 


0.38752 


1.29237 


1.67989 


264 


1168.14 


857.10 


1090.66 


0.38893 


1.28963 


1.67856 


265 


1168.46 


856.32 


1090.90 


0.39033 


1.28689 


1.67722 


266 


1168.78 


855.55 


1091.14 


0.39173 


1.28416 


1.67589 


267 


1169.11 


854.78 


1091.39 


0.39313 


1.28143 


1.67456 


268 


1169.43 


854.00 


1091.63 


0.39453 


1.27871 


1.67324 


269 


1169.75 


853.22 


1091.87 


0.39593 


1.27600 


1.67193 


270 


1170.07 


852.44 


1092.11 


0.39733 


1.27329 


1.67062 


271 


1170.38 


85.1.66 


1092.34 


0.39873 


1.27059 


1.66932 


272 


1170.70 


850.88 


1092.58 


0.40012 


1.26789 


1.66801 


273 


1171.01 


850,10 


1092.82 


0.40151 


1.26520 


1.66671 


274 


1171.32 


849.31 


1093.05 


0.40290 


1.26252 


1.66542 


275 



590 THE STEAM ENGINE AND TURBINE. 

Table II. Principal Steam Table 






l 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/p 


ft 


Q 


r 


275 


45.40 


9.315 


9.637 


.013119 


0.3023 


243.88 


927.44 


276 


46.14 


9.175 


9.495 


.012909 


0.3007 


244.90 


926.73 


277 


46.89 


9.037 


9.356 


.012703 


0.2991 


245.92 


926.02 


278 


47.64 


8.902 


9.219 


.012501 


0.2976 


246.95 


925.30 


279 


48.41 


8.770 


9.086 


.012303 


0.2960 


247.97 


924.59 


280 


49.19 


8.640 


8.955 


.012108 


0.2945 


248.99 


923.88 


281 


49.98 


8.512 


8.826 


.011917 


0.2930 


250.01 


923.16 


282 


50.78 


8.386 


8.698 


.011730 


0.2914 


251.03 


922.45 


283 


51.58 


8.263 


8.574 


.011546 


0.2899 


252.06 


921.73 


284 


52.40 


8.142 


8.451 


.011366 


0.2884 


253.08 


921.01 


285 


53.23 


8.023 


8.331 


.011189 


0.2869 


254.11 


920.29 


286 


54.07 


7.906 


8.213 


.011015 


0.2854 


255.13 


919.57 


287 


54.92 


7.791 


8.096 


.010844 


0.2839 


256.15 


918.84 


288 


55.78 


7.678 


7.982 


.010677 


0.2824 


257.18 


918.12 


289 


56.65 


7.567 


7.870 


.010513 


0.2809 


258.20 


917.39 


290 


57.53 


7.458 


7.760 


.010352 


0.2794 


259.23 


916.67 


291 


58.43 


7.351 


7.652 


.010194 


0.2780 


260.26 


915.94 


292 


59.33 


7.246 


7.545 


.010039 


0.2765 


261.28 


915.21 


293 


60.25 


7.142 


7.540 


.009887 


0.2751 


262.31 


914.48 


294 


61.18 


7.040 


7.337 


.009737 


0.2736 


263.34 


913.75 


295 


62.11 


6.940 


7.236 


.009590 


0.2722 


264.36 


913.02 


296 


63.06 


6.842 


7.137 


.009446 


0.2707 


265.39 


912.28 


297 


64.02 


6.745 


7.039 


.009304 


0.2693 


266.42 


911.55 


298 


65.00 


6.650 


6.942 


.009164 


0.2679 


267.45 


910.81 


299 


65.99 


6.556 


6.847 


.009027 


0.2664 


268.47 


910.08 


300 


66.98 


6.464 


6.754 


.008892 


0.2650 


269.50 


909.34 


301 


67.99 


6.373 


6.662 


.008760 


0.2636 


270.53 


908.60 


302 


69.01 


6.284 


6.572 


.008630 


0.2622 


271.56 


907.86 


303 


70.05 


6.197 


6.483 


.008503 


0.2608 


272.59 


907.11 


304 


71.09 


6.111 


6.396 


.008378 


0.2594 


273.61 


906.37 


305 


72.15 


6.027 


6.311 


.008255 


0.2580 


274.64 


905.62 


306 


73.22 


5.944 


6.227 


.008134 


0.2566 


275.67 


904.88 


307 


74.31 


5.862 


6.144 


.008015 


0.2553 


276.70 


904.13 


308 


75.40 


5.782 


6.063 


.007898 


0.2539 


277.73 


903.38 


309 


76.51 


5.703 


5.983 


.007784 


0.2515 


278.76 


902.63 


310 


77.64 


5.625 


5.904 


.007672 


0.2512 


279.79 


901.88 


311 


78.77 


5.548 


5.826 


.007561 


0.2498 


280.82 


901.12 


312 


79.92 


5.473 


5.749 


.007452 


0.2485 


281.85 


900.36 


313 


81.08 


5.399 


5.674 


.007345 


0.2472 


282.89 


899.60 


314 


82.26 


5.326 


5.600 


.007240 


0.2458 


283.92 


898.84 


315 


83.45 


5.255 


5.528 


.007137 


0.2445 


284.95 


898.08 


316 


84.65 


5.185 


5.457 


.007036 


0.2432 


285.98 


897.32 


317 


85.87 


5.115 


5.387 


.006936 


0.2419 


287.02 


896.55 


318 


87.10 


5.047 


5.317 


.006838 


0.2406 


288.05 


895.79 


319 


88.34 


4.980 


5.249 


.006742 


0.2393 


289.08 


895.03 


320 


89.60 


4.914 


5.182 


.006647 


0.2380 


290.11 


894.26 


321 


90.87 


4.849 


5.116 


.006554 


0.2367 


291.15 


893.49 


322 


92.16 


4.785 


5.051 


.006463 


0.2354 


292.18 


892.72 


323 


93.46 . 


4.722 


4.987 


.006373 


0.2341 


293.21 


891.95 


324 


94.78 


4.660 


4.924 


.006248 


0.2328 


294.25 


891.17 


325 


96.11 


4.599 


4.862 


.006197 


0.2315 


' 295.28 


890.40 






APPENDIX. 
Principal Steam Table 



591 
Table II. 



8 


9 


10 


11 


12 


13 





H 


I 


K 


a 


b 


N 


t 


1171.32 


849.31 


1093.05 


0.40290 


1.26252 


1.66542 


275 


1171.63 


848.53 


1093.28 


0.40429 


1.25984 


1.66413 


276 


1171.94 


847.74 


1093.51 


0.40568 


1.25717 


1.66285 


277 


1172.25 


846.95 


1093.75 


0.40707 


1.25450 


1.66157 


278- 


1172.56 


846.16 


1093.98 


0.40845 


1.25183 


1.66028 


279 


1172.87 


845.38 


1094.21 


0.40983 


1.24917 


1.65900 


280 


1173.17 


844.59 


1094.44 


0.41121 


1.24652 


1.65773 


281 


1173.48 


843.80 


1094.67 


0.41259 


1.24387 


1.65646 


282 


1173.79 


843.01 


1094.90 


0.41397 


1.24123 


1.65520 


283 


1174.09 


842.22 


1095.13 


0.41535 


1.23859 


1.65394 


284 


1174.40 


841.42 


1095.36 


0.41672 


1.23596 


1.65268 


285 


1174.70 


840.63 


1095.59 


0.41810 


1.23333 


1.65143 


286 


1175.00 


839.83 


1095.81 


0.41947 


1.23071 


1.65018 


287 


1175.30 


839.03 


1096.03 


0.42084 


1.22810 


1.64894 


288 


1175.60 


838.23 


1096.26 


0.42221 


1.22549 


1.64770 


289 


1175.90 


837.44 


1096.48 


0.42358 


1.22289 


1.64647 


290 


1176.20 


836.64 


1096.71 


0.42495 


1.22029 


1.64524 


291 


1176.49 


835.84 


1096.93 


0.42632 


1.21770 


1.64402 


292 


1176.79 


835.04 


1097.16 


0.42768 


1.21511 


1.64279 


293 


1177.09 


834.24 


1097.38 


0.42904 


1.21253 


1.64157 


294 


1177.38 


833.44 


1097.60 


0.43040 


1.20995 


1.64035 


295 


1177.67 


832.63 


1097.82 


0.43176 


1.20738 


1.63914 


296 


1177.97 


831.83 


1098.05 


0.43312 


1.20481 


1.63793 


297 


1178.26 


831.03 


1098.27 


0.43448 


1.20225 


1.63673 


298 


1178.55 


830.23 


1098.49 


0.43584 


1.19969 


1.63553 


299 


1178.84 


829.42 


1098.70 


0.43719 


1.19713 


1.63432 


300 


1179.13 


828.61 


1098.92 


0.43854 


1.19458 


1.63312 


301 


1179.42 


827.80 


1099.14 


0.43989 


1 . 19204 


1 . 63193 


302 


1179.70 


826.99 


1099.35 


0.44124 


1.18950 


1.63074 


303 


1179.98 


826.18 


1099.66 


0.44259 


1.18697 


1.62956 


304 


1180.26 


825.36 


1099.87 


0.44394 


1.18444 


1.62838 


305 


1180.55 


824.55 


1099.99 


0.44529 


1.18192 


1.62721 


306 


1180.83 


823.74 


1100.20 


0.44664 


1 . 17940 


1.62604 


307 


1181.11 


822.93 


1100.42 


0.44798 


1 . 17689 


1.62487 


308 


1181.39 


822.12 


1100.63 


0.44932 


1.17438 


1.62370 


309 


1181.67 


821.30 


1100.84 


0.45066 


1.17187 


1.62253 


310 


1181.94 


820.48 


1101.04 


0.45200 


1 . 16937 


1.62137 


311 


1182.21 


819.66 


1101.25 


0.45334 


1 . 16688 


1.62022 


312 


1182.49 


818.83 


1101.46 


0.45468 


1.16439 


1.61907 


313 


1182.76 


818.01 


1101.66 


0.45602 


1.16190 


1.61792 


314 


1183.03 


817.19 


1101.87 


0.45735 


1.15942 


1.61677 


315 


1183.30 


816.37 


1102.07 


0.45868 


1 . 15695 


1.61563 


316 


1183.57 


815.53 


1102.27 


0.46001 


1 . 15448 


1.61449 


317 


1183.84 


814.71 


1102.48 


0.46134 


1.15201 


1.61335 


318 


1184.11 


813.89 


1102.68 


0.46267 


1 . 14955 


1.61222 


319 


1184.37 


813.06 


1102.88 


0.46400 


1 . 14709 


1.61109 


320 


1184.64 


812.23 


1103.08 


0.46533 


1 . 14464 


1.60997 


321 


1184.90 


811.40 


1103.28 


0.46666 


1.14219 


1 . 60885 


322 


1185.16 


810.57 


1103.47 


0.46798 


1 . 13975 


1.60773 


323 


1185.42 


809.74 


1103.67 


0.46930 


1.13731 


1.60661 


324 


1185.68 


808.91 


1103.87 


0.47062 


1 . 13487 


1.60549 


325 



592 . THE STEAM ENGINE AND TURBINE. 

Table II. Principal Steam Table 






l 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/p 


ft 


0. 


r 


325 


96.11 


4.599 


4.862 


.006197 


0.2315 


295.28 


890.40 


326 


97.46 


4.539 


4.801 


.006111 


0.2302 


296.32 


889.62 


327 


98.82 


4.480 


4.741 


.006027 


0.2290 


297.35 


888.85 


328 


100.19 


4.422 


4.682 


.005944 


2277 


298.39 


888.07 


329 


101.58 


4.365 


4.624 


.005863 


0.2264 


299.43 


887.29 


330 


102.99 


4.308 


4.566 


.005783 


0.2252 


300.47 


886.51 


331 


104.41 


4.253 


4.510 


.005704 


0.2239 


301.50 


885.73 


332 


105.85 


4.3,98 


4.454 


: 005627 


0.2227 


302.54 


884.94 


333 


107.30 


4.144 


4.399 


.005551 


0.2215 


303.58 


884.15 


334 


108.77 


4.091 


4.345 


.005476 


0.2202 


304.62 


883.37 


335 


110.25 


4.039 


4.293 


.005402 


0.2190 


305.66 


882.58 


336 


111.75 


3.988 


4.241 


.005329 


0.2178 


306.70 


881.79 


337 


113.27 


3.937 


4.189 


.005258 


0.2166 


307.74 


881.00 


338 


114.80 


3.887 


4.138 


.005188 


0.2154 


308.78 


880.20 


339 


116.35 


3.838 


4.088 


.005119 


0.2142 


309.82 


879.41 


340 


117.92 


3.790 


4.039 


.005051 


0.2130 


310.86 


878.61 


341 


119.50 


3.742 


3.990 


.004984 


0.2118 


31L90 


877.81 


342 


121.10 


3.695 


3.942 


.004918 


0.2106 


312.95 


877.01 


343 


122.72 


3.649 


3.895 


.004853 


0.2094 


313.99 


876.21 


344 


124.35 


3.604 


3.849 


.004789 


0.2083 


315.03 


875.40 


345 


126.00 


3.559 


3.804 


.004727 


0.2071 


316.07 


874.60 


346 


127.67 


3.515 


3.759 


.004665 


0.2059 


317.11 


873.80 


347 


129.35 


3.472 


3.715 


.004604 


0.2048 


318.16 


872.99 


348 


131.05 


3.429 


3.671 


.004545 


0.2036 


319.20 


872.18 


349 


132.77 


3.387 


3.628 


.004486 


0.2024 


320.24 


871.37 


350 


134.51 


3.345 


3.585 


.004428 


0.2013 


321.28 


870.56 


351 


136.26 


3.304 


3.532 


.004371 


0.2001 


322.33 


869.74 


352 


138.03 


3.264 


3.502 


.004315 


0.1990 


323.37 


868.93 


353 


139.83 


3.224 


3.461 


.004260 


0.1979 


324.41 


868.12 


354 


141.64 


3.185 


3.421 


.004205 


0.1967 


325.46 


867.30 


355 


143.47 


3.146 


3.382 


.004151 


0.1956 


326.50 


866.48 


356 


145.32 


3.108 


3.343 


.004098 


0.1945 


327.55 


865.66 


357 


147.18 


3.071 


3.305 


.004046 


0.1933 


328.50 


864.83 


358 


149.06 


3.034 


3.267 


.003995 


0.1922 


329.64 


864.01 


359 


150.96 


2.997 


3.230 


.003945 


0.1911 


330.69 


863.19 


360 


152.88 


2.962 


3.193 


.003896 


0.1900 


331.74 


862.36 


361 


154.82 


2.926 


3.157 


.003847 


0.1889 


332.79 


861.53 


362 


156.78 


2.891 


3.121 


.003799 


0.1878 


333.83 


860.70 


363 


158.76 


2.857 


3.086 


.003752 


0.1867 


334.88 


859.87 


364 


160.76 


2.823 


3.051 


.003707 


0.1857 


335.93 


859.03 


365 


162.78 


2.790 


3.017 


.003659 


0.1846 


336.98 


858.20 


366 


164.82 


2.757 


2.983 


.003614 


0.1835 


338.03 


857.36 


367 


166.88 


2.724 


2.950 


.003570 


0.1824 


339.08 


856.52 


368 


168.96 


2.692 


2.917 


.003526 


0.1814 


340.13 


855.68 


369 


171.06 


2.661 


2.885 


.003482 


0.1803 


341.18 


854. '84 


370 


173.18 


2.630 


2.853 


.003439 


0.1792 


342.23 


854.00 


371 


175.32 


2.599 


2.822 


.003397 


0.1782 


343.28 


853.15 


372 


177.48 


2.569 


2.791 


.003356 


0.1772 


344.33 


852.31 


373 


179.66 


2.539 


2.760 


.003315 


0.1761 


345.39 


851.46 


374 


181.86 


2.510 


2.730 


.003275 


0.1751 


346.44 


850.61 


375 


184.09 


2.481 


2.700 


.003235 


0.1741 


347.49 


849.76 



APPENDIX. 
Principal Steam Table 



593 
Table II. 



8 


9 


10 


11 


12 


13 





H 


l 


K 


a 


b 


N 


t 


1185.68 


808.91 


1103.87 


0.47062 


1.13487 


1.60549 


325 


1185.94 


808.07 


1104.07 


0.47194 


1.13244 


1.60438 


326 


1186.20 


807.24 


1104.27 


0.47326 


1.13001 


1.60327 


327 


1186.46 


806.40 


1104.46 


0.47458 


1.12759 


1.60217 


328 - 


1186.72 


805.56 


1104.66 


0.47589 


1.12517 


1.60106 


329 


1186.98 


804.73 


1104.86 


0.47720 


1.12275 


1.59995 


330 


1187.23 


803.89 


1105.05 


0.47851 


1.12034 


1.59885 


331 


1187.48 


803.05 


1105.24 


0.47982 


1.11793 


1.59775 


332 


1187.73 


802.21 


1105.43 


0.48113 


1.11553 


1.59666 


333 


1187.99 


801.37 


1105.62 


0.48244 


1.11313 


1.59557 


334 


1188.24 


800.52 


1105.82 


0.48375 


1.11074 


1.59449 


335 


1188.49 


799.68 


1106.01 


0.48506 


1.10835 


1.59341 


336 


1188.74 


798.83 


1106.20 


0.48636 


1 . 10596 


1.59232 


337 


1188.98 


797.98 


1106.38 


0.48767 


1.10358 


1.59125 


338 


1189.23 


797.13 


1106.57 


0.48897 


1.10120 


1.59017 


339 


1189.47 


796.28 


1106.75 


0.49027 


1.09883 


1.58910 


340 


1189.71 


795.43 


1106.94 


0.49157 


1.09646 


1.58803 


341 


1189.96 


794.58 


1107.13 


0.49287 


1.09409 


1.58696 


342 


1190.20 


793.73 


1107.31 


0.49417 


1.09173 


1.58590 


343 


1190.43 


792.87 


1107.49 


0.49547 


1.08937 


1.58484 


344 


1190.67 


792.02 


1107.67 


0.49676 


1.08702 


1.58378 


345 


1190.91 


791.17 


1107.85 


0.49806 


1.08467 


1.58273 


346 


1191.15 


790.31 


1108.03 


0.49935 


1.08232 


1.58167 


347 


1191.38 


789.45 


1108.21 


0.50064 


1.07998 


1.58062 


348 


1191.61 


788.59 


1108.39 


0.50193 


1.07764 


1.57957 


349 


1191.84 


787.73 


1108.56 


0.50322 


1.07531 


1.57853 


350 


1192.07 


786.87 


1108.74 


0.50451 


1.07298 


1.57749 


351 


1192.30 


786.01 


1108.92 


0.50580 


1.07065 


1.57645 


352 


1192.53 


785.15 


1109.09 


0.50708 


1.06833 


1.57541 


353 


1192.76 


784.28 


1109.27 


0.50837 


1.06601 


1.57438 


354 


1192.98 


783.42 


1109.44 


0.50965 


1.06369 


1.57334 


355 


1193.21 


782.55 


1109.61 


0.51093 


1.06138 


1.57231 


356 


1193.43 


781.67 


1109.78 


0.51221 


1.05907 


1.57128 


357 


1193.65 


780.81 


1109.95 


0.51349 


1.05677 


1.57026 


358 


1193.88 


779.95 


1110.13 


0.51477 


1.05447 


1.56924 


359 


1194.10 


779.07 


1110.30 


0.51605 


1.05217 


1.56822 


360 


1194.32 


778.20 


1110.47 


0.51733 


1.04988 


1.56721 


361 


1194.53 


777.33 


1110.63 


0.51860 


1.04759 


1.56619 


362 


1194.75 


776.46 


1110.80 


0.51988 


1.04530 


1.56518 


363 


1194.96 


775.57 


1110.96 


0.52115 


1.04302 


1.56417 


364 


1195.18 


774.70 


1111.13 


0.52242 


1.04074 


1.56316 


365 


1195.39 


773.82 


1111.29 


0.52369 


1.03847 


1.56216 


366 


1195.60 


772.94 


1111.46 


0.52496 


1.03620 


1.56116 


367 


1195.81 


772.06 


1111.62 


0.52623 


1.03393 


1.56016 


368 


1196 02 


771 . 18 


1111.78 


0.52750 


1.03167 


1.55917 


369 


1196.23 


770.30 


1111.94 


0.52877 


1.02941 


1.55818 


370 


1196.43 


769.41 


1112.10 


0.53004 


1.02715 


1.55719 


371 


1196.64 


768.53 


1112.26 


0.53130 


1.02490 


1.55620 


372 


1196.85 


767.65 


1112.43 


0.53257 


1.02265 


1 . 55522 


373 


1197.05 


766.76 


1112.58 


0.53383 


1.02040 


1 . 55423 


374 


1197.25 


765.87 


1112.74 


0.53509 


1.01816 


1.55325 


375 



594 THE STEAM ENGINE AND TURBINE 

Table II. Principal Steam Table 






l 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/v 


h 


Q 


r 


375 


184.09 


2.481 


2.700 


.003235 


0.1741 


347.49 


849.76 


376 


186.33 


2.452 


2.671 


.003196 


0.1730 


348.55 


848.90 


377 


188.60 


2.424 


2.642 


.003158 


0.1720 


349.60 


848.05 


378 


190.88 


2.396 


2.613 


.003120 


0.1710 


350.65 


847.19 


379 


193.19 


2.369 


2.585 


.003083 


0.1700 


351.70 


846.34 


380 


195.52 


2.342 


2.558 


.003046 


0.1689 


352.76 


845.48 


381 


197.87 


2.315 


2.530 


.003010 


0.1679 


353.82 


844.62 


382 


200.25 


2.289 


2.503 


.002974 


0.1669 


354.87 


843.76 


383 


202.65 


2.263 


2.476 


.002939 


0.1659 


355.93 


842.89 


384 


205.07 


2.237 


2.450 


.002905 


0.1649 


356.98 


842.03 


385 


207.51 


2.212 


2.424 


.002870 


0.1639 


358.04 


841.16 


386 


209.97 


2.187 


2.398 


.002837 


0.1629 


359.10 


840.29 


387 


212.46 


2.162 


2.373 


.002803 


0.1619 


360.16 


839.42 


388 


214.97 


2.138 


2.348 


.002771 


0.1609 


361.22 


838.54 


389 


217.50 


2.114 


2.324 


.002737 


0.1600 


362.27 


837.67 


390 


220.06 


2.090 


2.299 


.002707 


0.1590 


363.33 


836.79 


391 


222.64 


2.067 


2.275 


.002675 


0.1580 


364.39 


835.91 


392 


225.24 


2.044 


2.252 


.002644 


0.1571 


365.45 


835.03 


393 


227.87 


2.021 


2.228 


.002614 


0.1561 


366.51 


834.15 


394 


230.52 


1.999 


2.205 


.002584 


0.1552 


367.57 


833.26 


395 


233.19 


1.977 


2.183 


.002554 


0.1543 


368.63 


832.38 


396 


235.89 


1.955 


2.160 


.002525 


0.1533 


369.69 


831.49 


397 


238.61 


1.934 


2.138 


.002496 


0.1524 


370.76 


830.60 


398 


241.36 


1.912 


2.116 


.002468 


0.1515 


371.82 


829.71 . 


399 


244.13 


1.892 


2.095 


.002440 


0.1506 


372.88 


828.81 


400 


246.93 


1.871 


2.073 


.002412 


0.1497 


373.94 


827.92 


401 


249.75 


1.850 


2.052 


.002385 


0.1488 


375.01 


827.02 


402 


252.60 


1.830 


2.032 


.002358 


0.1479 


376.07 


826.12 


403 


255.47 


1.810 


2.011 


.002331 


0.1470 


377.13 


825.22 


404 


258.37 


1.791 


1.991 


.002305 


0.1461 


378.20 


824.31 


405 


261.29 


1.771 


1.971 


.002280 


0.1452 


379.26 


823.41 


406 


264.24 


1.752 


1.951 


.002254 


0.1443 


380.33 


822.50 


407 


267.22 


1.733 


1.932 


.002239 


0.1434 


381.39 


821.59 


408 


270.22 


1.715 


1.912 


.002204 


0.1425 


382.46 


820.68 


409 


273.25 


1.696 


1.893 


.002180 


0.1417 


383.53 


819.77 


410 


276.30 


1.678 


1.875 


.002156 


0.1408 


384.59 


818.86 


411 


279.38 


1.660 


1.856 


.002132 


0.1399 


385.66 


817.94 


412 


282.48 


1.643 


1.838 


.002108 


0.1391 


386.73 


817.02 


413 


285.61 


1.625 


1.820 


.002085 


0.1382 


387.80 


816.10 


414 


288.77 


1.608 


1.802 


.002063 


0.1374 


388.86 


815.18 


415 


291.96 


1.591 


1.784 


.002040 


0.1365 


389.93 


814.25 


416 


295.17 


1.574 


1.767 


.002018 


0.1357 


391.00 


813.33 


417 


298.41 


1.557 


1.750 


.001996 


0.1349 


392.07 


812.40 


418 


301.68 


1.541 


1.733 


.001974 


0.1340 


393.14 


811.47 


419 


304.98 


1.525 


1.716 


.001953 


0.1332 


394.21 


810.54 


420 


308.30 


1.509 


1.699 


.001932 


0.1324 


395.28 


809.61 


421 


311.65 


1.493 


1.683 


.001911 


0.1316 


396.36 


808.67 


422 


315.03 


1.477 


1.667 


.001891 


0.1308 


397.43 


807.73 


423 


318.44 


1.462 


1.651 


.001870 


0.1300 


398.50 


806.79 


424 


321.88 


1.447 


1.635 


.001850 


0.1292 


399.57 


805.85 


425 


325.34 


1.432 


1.620 


.001831 


0.1284 


400.65 


804.90 



APPENDIX. 
Principal Steam Table 



595 
Table II. 



8 


9 


10 


11 


12 


13 





H 


I 


K 


a 


b 


N 


t 


1197.25 


765.87 


1112.74 


0.53509 


1.01816 


1.55325 


375 


1197.45 


764.97 


1112.89 


0.53635 


1.01592 


1.55227 


376 


1197.65 


764.09 


1113.05 


0.53761 


1.01368 


1.55129 


377 


1197.84 


763.20 


1113.20 


0.53887 


1.01145 


1.55032 


378 


1198.04 


762.31 


1113.35 


0.54013 


1.00922 


1.54935 


379 


1198.24 


761.41 


1113.50 


0.54139 


1.00700 


1.54839 


380 


1198.44 


760.52 


1113.66 


0.54265 


1.00478 


1.54743 


381 


1198.63 


759.62 


1113.81 


0.54390 


1.00256 


1.54646 


382 


1198.82 


758.72 


1113.96 


0.54516 


1.00034 


1.54550 


383 


1199.01 


757.83 


1114.11 


0.54641 


0.99813 


1.54454 


384 


1199.20 


756.93 


1114.26 


0.54766 


0.99592 


1.54358 


385 


1199.39 


756.03 


1114.41 


0.54891 


0.99371 


1.54262 


386 


1199.58 


755.13 


1114.56 


0.55016 


0.99151 


1.54167 


387 


1199.76 


754.22 


1114.70 


0.55141 


0.98931 


1.54072 


388 


1199.94 


753.32 


1114.84 


0.55266 


0.98711 


1.53977 


389 


1200.12 


752 .41 


1114.98 


0.55391 


0.98492 


1.53883 


390 


1200.30 


751.50 


1115.12 


0.55516 


0.98273 


1.53789 


391 


1200.48 


750.59 


1115.26 


0.55640 


0.98054 


1.53694 


392 


1200.66 


749.68 


1115.40 


0.55765 


0.97835 


1.53600 


393 


1200.83 


748.76 


1115.54 


0.55889 


0.97617 


1.53506 


394 


1201.01 


747.85 


1115.68 


0.56013 


0.97399 


1.53412 


395 


1201 . 18 


746.94 


1115.82 


0.56137 


0.97181 


1.53318 


396 


1201.36 


746.02 


1115.96 


0.56261 


0.96964 


1.53225 


397 


1201.53 


745.10 


1116.09 


0.56385 


0.96747 


1.53132 


398 


1201 . 69 


744.18 


1116.22 


0.56509 


0.96530 


1.53039 


399 


1201.86 


743.27 


1116.35 


0.56633 


0.96314 


1.52947 


400 


1202.03 


742.35 


1116.49 


0.56757 


0.96098 


1.52855 


401 


1202.19 


741 . 43 


1116.62 


0.56880 


0.95882 


1.52762 


402 


1202.35 


740.50 


1116.74 


0.57004 


0.95666 


1.52670 


403 


1202.51 


739.57 


1116.87 


0.57127 


0.95451 


1.52578 


404 


1202.67 


738.65 


1117.00 


0.57250 


0.95236 


1.52486 


405 


1202.83 


737.72 


1117.13 


0.57373 


0.95021 


1.52394 


406 


1202.98 


736.79 


1117.25 


0.57496 


0.94807 


1.52303 


407 


1203.14 


735.86 


1117.38 


0.57619 


0.94593 


1.52212 


408 


1203.30 


734.93 


1117.51 


0.57742 


0.94379 


1.52121 


409 


1203.45 


734.01 


1117.63 


0.57865 


0.94165 


1.52030 


410 


1203.60 


733.07 


1117.75 


0.57988 


0.93952 


1.51940 


411 


1203.75 


732.13 


1117.87 


0.58111 


0.93739 


1.51850 


412 


1203.90 


731.19 


1117.99 


0.58233 


0.93526 


1.51759 


413 


1204.04 


730.26 


1118.11 


0.58356 


0.93313 


1.51669 


414 


1204.18 


729.31 


1118.22 


0.58478 


0.93101 


1.51579 


415 


1204.33 


728.38 


1118.34 


0.58600 


0.92889 


1.51489 


416 


1204.47 


727.44 


1118.46 


0.58722 


0.92677 


1.51399 


417 


1204.61 


726.49 


1118.57 


0.58844 


0.92466 


1.51310 


418 


1204.75 


725.55 


1118.69 


0.58966 


0.92255 


1.51221 


419 


1204.89 


724.61 


1118.81 


0.59088 


0.92044 


1.51132 


420 


1205.03 


723.66 


1118.92 


0.59210 


0.91833 


1.51043 


421 


1205.16 


722.71 


1119.03 


0.59332 


0.91632 


1.50955 


422 


1205.29 


721.76 


1119.14 


0.59453 


0.91413 


1.50866 


423 


1205.42 


720.81 


1119.24 


0.59575 


0.91203 


1.50778 


424 


1205.55 


719.85 


1119.35 


0.59697 


0.90993 


1.50690 


425 



596 THE STEAM ENGINE AND TURBINE 

Table II. Principal Steam Table 






l 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/P 


ft 


Q 


r 


425 


325.3 


1.432 


1.620 


.001831 


0.1284 


400.65 


804.90 


426 


328.8 


1.417 


1.604 


.001811 


0.1276 


401.72 


803.96 


427 


332.4 


1.402 


1.589 


.001792 


0.1268 


402.79 


803.01 


428 


335.9 


1.387 


1.574 


.001773 


0.1260 


403.87 


802.06 


429 


339.5 


1.373 


1.559 


.001755 


0.1252 


404.94 


801.11 


430 


343.1 


1.359 


1.544 


.001736 


0.1244 


406.02 


800.16 


431 


346.7 


1.345 


1.530 


.001718 


0.1237 


407.10 


799.20 


432 


350.4 


1.331 


1.516 


.001700 


0.1229 


408.17 


798.24 


433 


354.1 


1.317 


1.501 


.001682 


0.1221 


409.25 


797.28 


434 


357.8 


1.304 - 


1.487 


.001665 


0.1214 


410.33 


796.32 


435 


361.6 


1.291 


1.474 


.001647 


0.1206 


411.41 


795.35 


436 


365.4 


1.278 


1.460 


.001630 


0.1199 


412.48 


794.39 


437 


369.2 


1.265 


1.446 


.001613 


0.1191 


413.56 


793.42 


438 


373.0 


1.252 


1.433 


.001597 


0.1184 


-414.64 


792.45 


439 


376.9 


1.239 


1.420 


.001580 


0.1177 


415.72 


791.48 


440 


380.8 


1.227 


1.407 


.001564 


0.1169 


416.80 


790.50 


441 


384.8 


1.214 


1.394 


.001548 


0.1162 


417.88 


789.52 


442 


388.7 


1.202 


1.382 


.001532 


0.1155 


418.96 


788.54 


443 


392.7 


1.190 


1.369 


.001517 


0.1148 


420.04 


787.56 


444 


396.8 


1.178 


1.357 


.001491 


0.1140 


421.13 


786.57 


445 


400.8 


1.166 


1.344 


.001486 


0.1133 


422.21 


785.59 


446 


404.9 


1.154 


1.332 


.001471 


0.1126 


423.29 


784.60 


447 


409.1 


1.143 


1.320 


.001456 


0.1119 


424.37 


783.61 


448 


413.2 


1.131 


1.308 


.001441 


0.1112 


425.46 


782.61 


449 


417.4 


1.120 


1.297 


.001427 


0.1105 


426.54 


781.62 


450 


421.7 


1.109 


1.285 


.001413 


0.1098 


427.63 


780.62 


451 


425.9 


1.098 


1.273 


". 001398 


0.1091 


428.71 


779.62 


452 


430.2 


1.087 


1.262 


.001384 


0.1084 


429.80 


778.61 


453 


434.6 


1.076 


1.251 


.001371 


.0.1077 


430.88 


777.61 


454 


438.9 


1.066 


1.240 


.001357 


0.1070 


431.97 


776.60 


455 


443.3 


1.055 


1.229 


.001344 


0.1064 


433.05 


775.59 


456 


447.7 


1.045 


1.218 


.001330 


0.1057 


434.14 


774.58 


457 


452.2 


1.034 


1.207 


.001317 


0.1050 


435.23 


773.56 


458 


456.7 


1.024 


1.197 


.001304 


0.1044 


436.32 


772.54 


459 


461.2 


1.014 


1.186 


.001291 


0.1037 


437.41 


771.52 


460 


465.8 


1.004 


1.176 


.001279 


0.1031 


438.50 


770.50 


461 


470.4 


0.994 


1.166 


.001266 


0.1024 


439.59 


769.47 


462 


475.0 


0.985 


1.156 


.001254 


0.1018 


440.68 


768.45 


463 


479.7 


0.975 


1.146 


.001242 


0.1011 


441.77 


767.42 


464 


484.4 


0.966 


1.136 


.001230 


0.1005 


442.86 


766.39 


465 


489.1 


0.956 


1.126 


.001218 


0.0999 


443.96 


765.35 


466 


493.9 


0.947 


1.116 


.001206 


0.0992 


445.05 


764.31 


467 


498.7 


0.938 


1.107 


.001194 


0.0986 


446.14 


763.27 


468 


503.6 


0.929 


1.097 


.001183 


0.0980 


447.23 


762.23 


469 


508.5 


0.920 


1.088 


.001171 


0.0974 


448.33 


761.18 


470 


513.4 


0.911 


1.079 


.001160 


0.0968 


449.42 


760.13 


471 


518.3 


0.902 


1.069 


.001149 


0.0962 


450.52 


759.08 


472 


523.3 


0.893 


1.060 


.001138 


0.0956 


451.61 


758.03 


473 


528.4 


0.885 


1.051 


.001127 


0.0950 


452.71 


756.97 


474 


533.4 


0.876 


1.042 


.001117 


0.0944 


453.81 


755.91 


475 


538.5 


0.868 


1.034 


.001106 


0.0938 


454.90 


754.85 






APPENDIX. 
Principal Steam Table 



597 
Table II. 



8 


9 


10 


11 


12 


13 





H 


l 


K 


a 


b 


N 


t 


1205.55 


719.85 


1119.35 


0.59697 


0.90993 


1.50690 


425 


1205 . 68 


718.90 


1119.46 


0.59818 


0.90784 


1.50602 


426 


1205.80 


717.95 


1119.56 


0.59939 


0.90575 


1.50514 


427 


1205.93 


716.99 


1119.67 


0.60060 


0.90366 


1.50426 


428 ' 


1206.05 


716.03 


1119.77 


0.60181 


0.90157 


1.50338 


429 


1206.18 


715.08 


1119.88 


0.60302 


0.89948 


1.50250 


430 


1206.30 


714.12 


1119.98 


0.60423 


0.89740 


1.50163 


431 


1206.41 


713.15 


1120.08 


0.60544 


0.89532 


1.50076 


432 


1206.53 


712.19 


1120.18 


0.60665 


0.89324 


1.49989 


433 


1206.65 


711.23 


1120.29 


0.60785 


0.89116 


1.49901 


434 


1206.76 


710.26 


1120.38 


0.60906 


0.88908 


1.49814 


435 


1206.87 


709.30 


1120.48 


0.61026 


0.88701 


1.49727 


436 


1206.98 


708.33 


1120.57 


0.61147 


0.88494 


1.49641 


437 


1207.09 


707.36 


1120.67 


0.61267 


0.88287 


1.49554 


438 


1207.20 


706.39 


1120.76 


0.61387 


0.88080 


1.49467 


439 


1207.30 


705.41 


1120.85 


0.61507 


0.87874 


1.49381 


440 


1207.40 


704.44 


1120.94 


0.61627 


0.87668 


1.49295 


441 


1207.50 


703.46 


1121.03 


0.61747 


0.87462 


1.49209 


442 


1207.60 


702.48 


1121.12 


0.61867 


0.87256 


1.49123 


443 


1207.70 


701.50 


1121.21 


0.61987 


0.87050 


1.49037 


444 


1207.80 


700.53 


1121.30 


0.62106 


0.86845 


1.48951 


445 


1207.89 


699.55 


1121.38 


0.62226 


0.86640 


1.48866 


446 


1207.98 


698.56 


1121.46 


0.62346 


0.86435 


1.48781 


447 


1208.07 


697.57 


1121.54 


0.62465 


0.86230 


1.48695 


448 


1208.16 


696.59 


1121.62 


0.62585 


0.86025 


1.48610 


449 


1208.25 


695.60 


1121.70 


0.62704 


0.85821 


1.48525 


450 


1208.33 


694.61 


1121.78 


0.62823 


0.85617 


1.48440 


451 


1208.41 


693.61 


1121.85 


0.62943 


0.85413 


1.48356 


452 


1208.49 


692.62 


1121.93 


0.63062 


0.85209 


1.48271 


453 


1208.57 


691.63 


1122.00 


0.63181 


0.85006 


1.48187 


454 


1208.64 


690.63 


1122.07 


0.63300 


0.84802 


1 . 48102 


455 


1208.72 


689.63 


1122.15 


0.63419 


0.84599 


1.48018 


456 


1208.79 


688.63 


1122.22 


0.63537 


0.84396 


1.47933 


457 


1208.86 


687.63 


1122.29 


0.63656 


0.84193 


1.47849 


458 


1208.93 


686.63 


1122.36 


0.63775 


0.83990 


1 . 47765 


459 


1209.00 


685.63 


1122.43 


0.63893 


0.83787 


1.47680 


460 


1209.06 


684.62 


1122.49 


0.64011 


0.83585 


1.47596 


461 


1209.13 


683.62 


1122.56 


0.64130 


0.83382 


1.47512 


462 


1209.19 


682.61 


1122.63 


0.64248 


0.83180 


1.47428 


463 


1209.25 


681.60 


1122.69 


0.64366 


0.82978 


1.47344 


464 


1209.31 


680.59 


1122.76 


0.64484 


0.82776 


1.47260 


465 


1209.36 


679.57 


1122.81 


0.64602 


0.82574 


1.47176 


466 


1209.41 


678.56 


1122.87 


0.64720 


0.82373 


1.47093 


467 


1209.46 


677.54 


1122.92 


0.64838 


0.82171 


1.47009 


468 


1209.51 


676.52 


1122.98 


0.64956 


0.81970 


1.46926 


469 


1209.55 


675.49 


1123.03 


0.65074 


0.81769 


1.46843 


470 


1209.60 


674.47 


1123.08 


0.65192 


0.81568 


1.46760 


471 


1209.64 


673.45 


1123.13 


0.65310 


0.81367 


1.46677 


472 


1209.68 


672.42 


1123.18 


0.65427 


0.81167 


1.46594 


473 


1209.72 


671.39 


1123.23 


0.65545 


0.80966 


1.46511 


474 


1209.75 


670.36 


1123.27 


0.65662 


0.80766 


1.46428 


475 



598 


THE STEAM ENGINE AND TURBINE 




Table II. 


Principal Steam Table 









l 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/p 


ft 


Q 


r 


475 


538.5 


0.868 


1.034 


.001106 


0.0938 


454.9 


754.9 


476 


543.7 


0.859 


1.025 


.001096 


0.0932 


456.0 


753.8 


477 


548.9 


0.851 


1.016 


.001085 


0.0926 


457.1 


752.7 


478 


554.1 


0.843 


1.008 


.001075 


0.0920 


458.2 


751.6 


479 


559.3 


0.835 


1.000 


.001065 


0.0915 


459.3 


750.6 


480 


564.6 


0.827 


0.991 


.001055 


0.0909 


460.4 


749.5 


481 


570.0 


0.819 


0.983 


.001045 


0.0903 


461.5 


748.4 


482 


575.3 


0.811 


0.975 


.001035 


0.0898 


462.6 


747.3 


483 


580.7 


0.804 


0.967 


.001026 


0.0892 


463.7 


746.2 


484 


586.2 


0.796 


0.959 


.001016 


0.0886 


464.8 


745.2 


485 


591.7 


0.788 


0.951 


.001007 


0.0881 


465.9 


744.1 


486 


597.2 


0.781 


0.943 


.000997 


0.0875 


467.0 


743.0 


487 


602.8 


0.773 


0.935 


.000988 


0.0870 


468.1 


741.9 


488 


608.4 


0.766 


0.928 


.000979 


0.0864 


469.2 


740.8 


489 


614.1 


0.759 


0.920 


.000970 


0.0859 


470.3 


739.7 


490 


619.8 


0.752 


0.913 


.000961 


0.0853 


471.4 


738.6. 


491 


625.5 


0.745 


0.905 


.000952 


0.0848 


472.6 


737.4 


492 


631.3 


0.738 


0.898 


.000944 


0.0843 


473.7 


736.3 


493 


637.1 


0.731 


0.891 


.000935 


0.0837 


474.8 


735.2 


494 


643.0 


0.724 


0.883 


.000926 


0.0832 


475.9 


734.1 


495 


648.9 


0.717 


0.876 


.000918 


0.0827 


477.0 


733.0 


496 


654.8 


0.710 


0.869 


.000910 


0.0821 


478.1 


731.8 


497 


660.8 


0.704 


0.862 


.000901 


0.0816 


479.2 


730.7 


498 


666.8 


0.697 


0.855 


.000893 


0.0811 


480.3 


729.6 


499 


672.9 


0.691 


0.849 


.000885 


0.0805 


481.4 


728.4 


500 


679.0 


0.684 


0.842 


.000877 


0.0800 


482.5 


727.3 


501 


685.1 


0.678 


0.835 


.000869 


0.0795 


483.6 


726.1 


502 


691.3 


0.671 


0.828 


.000862 


0.0790 


484.7 


725.0 


503 


697.6 


0.665 


0.822 


.000854 


0.0785 


485.9 


723.8 
722.6 
721.5 


504 


703.9 


0.659 


0.815 


.000846 


0.0780 


487.0 


505 


710.2 


0.653 


0.809 


.000839 


0.0775 


488.1 


506 


716.6 


0.647 


0.803 


.000831 


0.0770 


489.2 


720.3 


507 


723.0 


0.641 


0.796 


.000824 


0.0765 


490.3 


719.1 


508 


729.5 


0.635 


0.790 


.000816 


0.0760 


491.4 


718.0 


509 


736.0 


0.629 


0.784 


.000809 


0.0755 


492.5 


716.8 


510 


742.5 


0.623 


0.778 


.000802 


0.0751 


493.6 


715.6 


511 


749.2 


0.617 


0.772 


.000795 


0.0746 


494.8 


714.4 


512 


755.8 


0.611 


0.766 


.000788 


0.0741 


495.9 


713.2 


513 


762.5 


0.606 


0.760 


.000781 


0.0737 


497.0 


712.0 


514 


769.2 


0.600 


0.754 


.000774 


0.0732 


498.1 


710.8 


515 


776.0 


0.595 


0.748 


.000768 


0.0727 


499.2 


709.6 


516 


782.9 


0.589 


0.742 


.000761 


0.0723 


500.4 


708.3 


517 


789.7 


0.584 


0.737 


.000754 


0.0718 


501.5 


707.1 


518 


796.7 


0.578 


0.731 


.000748 


0.0714 


502.6 


705.9 


519 


803.6 


0.573 


0.725 


.000741 


0.0709 


503.7 


704.7 


520 


810.7 


0.568 


0.720 


.000735 


0.0705 


504.9 


703.4 


521 


817.7 


0.562 


0.714 


.000728 


0.0700 


506.0 


702.2 


522 


824.8 


0.557 


0.709 


.000722 


0.0696 


507.1 


700.9 


523 


832.0 


0.552 


0.704 


.000716 


0.0692 


508.2 


699.7 


524 


839.2 


0.547 


0.698 


.000710 


0.0687 


509.4 


698.4 


525 


846.5 


0.542 


0.693 


.000704 


0.0683 


510.5 


697.1 



APPENDIX. 

Principal Steam Table 



599 
Table II. 



8 


9 


10 


n 


12 


13 





H 


l 


K 


a 


b 


N 


t 


1209.8 


670.4 


1123.3 


0.6566 


0.8077 


1.4643 


475 


1209.8 


669.3 


1123.3 


0.6578 


0.8057 


1.4635 


476 


1209.8 


668.3 


1123.4 


0.6590 


0.8037 


1.4627 


477- 


1209.8 


667.2 


1123.4 


0.6601 


0.8017 


1.4618 


478 


1209.9 


666.2 


1123.4 


0.6613 


0.7997 


1.4610 


479 


1209.9 


665.2 


1123.5 


0.6625 


0.7977 


1.4602 


480 


1209.9 


664.1 


1123.5 


0.6636 


0.7957 


1.4593 


481 


1209.9 


663.1 


1123.5 


0.6648 


0.7937 


1.4585 


482 


1209.9 


662.0 


1123.6 


0.6660 


0.7917 


1.4577 


483 


1210.0 


661.0 


1123.6 


0.6671 


0.7897 


1.4568 


484 


1210.0 


659.9 


1123.6 


0.6683 


0.7877 


1.4560 


485 


1210.0 


658.9 


1123.7 


0.6695 


0.7857 


1.4552 


486 


1210.0 


657.8 


1123.7 


0.6707 


0.7837 


1.4544 


487 


1210.0 


656.8 


1123.7 


0.6718 


0.7817 


1.4535 


488 


1210.0 


655.7 


1123.7 


0.6730 


0.7797 


1.4527 


489 


1210.0 


654.7 


1123.8 


0.6741 


0.7778 


1.4519 


490 


1210.0 


653.6 


1123.8 


0.6753 


0.7758 


1.4511 


491 


1210.0 


652.5 


1123.8 


0.6765 


0.7738 


1.4503 


492 


1210.0 


651.5 


1123.8 


0.6776 


0.7718 


1.4494 


493 


1210.0 


650.4 


1123.8 


0.6788 


0.7698 


1.4486 


494 


1209.9 


649.3 


1123.8 


0.6800 


0.7678 


1.4478 


495 


1209.9 


648.2 


1123.8 


0.6811 


0.7658 


1.4469 


496 


1209.9 


647.2 


1123.8 


0.6823 


0.7638 


1.4461 


497 


1209.9 


646.1 


1123.8 


0.6834 


0.7619 


1.4453 


498 


1209.8 


645.0 


1123.8 


0.6846 


0.7599 


1.4445 


499 


1209.8 


643.9 


1123.8 


0.6858 


0.7579 


1.4437 


500 


1209.7 


642.8 


1123.8 


0.6869 


0.7559 


1.4428 


501 


1209.7 


641.7 


1123.8 


0.6881 


0.7539 


1.4420 


502 


1209.7 


640.6 


1123.8 


0.6892 


0.7520 


1.4412 


503 


1209.6 


639.5 


1123.8 


0.6904 


0.7500 


1.4404 


504 


1209.6 


638.4 


1123.8 


0.6915 


0.7480 


1.4395 


505 


1209.5 


637.3 


1123.7 


0.6927 


0.7460 


1.4387 


506 


1209.4 


636.2 


1123.7 


0.6938 


0..7440 


1.4378 


507 


1209.4 


635.1 


1123.7 


0.6950 


0.7420 


1.4370 


508 


1209.3 


634.0 


1123.7 


0.6962 


0.7400 


1.4362 


509 


1209.2 


632.8 


1123.6 


0.6973 


0.7380 


1.4353 


510 


1209.2 


631.7 


1123.6 


0.6985 


0.7360 


1.4345 


511 


1209.1 


630.6 


1123.6 


0.6996 


0.7341 


1.4337 


512 


1209.0 


629.5 


1123.5 


0.7008 


0.7321 


1.4329 


513 


1208.9 


628.3 


1123.5 


0.7019 


0.7301 


1.4320 


514 


1208.8 


627.2 


1123.4 


0.7031 


0.7281 


1.4312 


515 


1208.7 


626.0 


1123.4 


0.7042 


0.7261 


1.4303 


516 


1208.6 


624.9 


1123.3 


0.7054 


0.7241 


1.4295 


517 


1208.5 


623.7 


1123.3 


0.7065 


0.7221 


1.4286 


518 


1208.4 


622.6 


1123.2 


0.7077 


0.7201 


1.4278 


519 


1208.3 


621.4 


1123.1 


0.7088 


0.7181 


1.4269 


520 


1208.2 


620.3 


1123.1 


0.7099 


0.7161 


1.4260 


521 


1208.0 


619.1 


1123.0 


0.7111 


0.7141 


1.4252 


522 


1207.9 


617.9 


1122.9 


0.7122 


0.7121 


1.4243 


523 


1207.8 


616.7 


1122.8 


0.7134 


0.7100 


1.4234 


524 


1207.6 


615.6 


1122.7 


0.7146 


0.7080 


1.4226 


525 



600 THE STEAM ENGINE AND TURBINE 

Table II. Pkincipal Steam Table 






l 


2 


3 


4 


5 


6 


7 


t 


V 


s 


s' 


R/P 


A 


9 


r 


525 


846.5 


0.542 


0.693 


.000704 


0.0683 


510.5 


697.1 


526 


853.8 


0.537 


0.688 


.000698 


0.0679 


511.6 


695.9 


527 


861.2 


0.532 


0.682 


.000692 


0.0674 


512.7 


694.6 


528 


868.6 


0.527 


0.677 


.000686 


0.0670 


513.9 


693.3 


529 


876.1 


0.522 


0.672 


.000680 


0.0666 


515.0 


692.0 


530 


883.6 


0.517 


0.667 


.000674 


0.0662 


516.1 


690.7 


531 


891.2 


0.513 


0.662 


.000668 


0.0657 


517.3 


689.4 


532 


898.8 


0.508 


0.657 


.000663 


0.0653 


518.4 


688.1 


533 


906.5 


0.503 


0.652 


.000657 


0.0649 


519.5 


686.8 


534 


914.2 


0.499 


0.647 


.000652 


0.0645 


520.7 


685.4 


535 


922.0 


0.494 


0.643 


.000646 


0.0641 


521.8 


684.1 


536 


929.8 


0.490 


0.638 


.000641 


0.0637 


523.0 


682.7 


537 


937.7 


0.485 


0.633 


.000635 


0.0632 


524.1 


681.4 


538 


945.6 


0.481 


0.628 


.000630 


0.0628 


525.2 


680.0 


539 


953.6 


0.476 


0.624 


.000625 


0.0624 


526.4 


678.6 


540 


961.6 


0.472 


0.619 


.000619 


0.0620 


527.5 


677.3 


541 


969.7 


0.468 


0.615 


.000614 


0.0616 


528.6 


675.9 


542 


977.9 


0.463 


0.610 


.000609 


0.0612 


529.8 


674.5 


543 


986.1 


0.459 


0.606 


.000604 


0.0608 


530.9 


673.1 


544 


994.3 


0.455 


0.601 


.000599 


0.0604 


532.1 


671.6 


545 


1002.6 


0.451 


0.597 


.000594 


0.0600 


533.2 


670.2 


546 


1011.0 


0.447 


0.593 


.000589 


0.0596 


534.4 


668.8 


547 


1019.4 


0.443 


0.588 


.000584 


0.0592 


535.5 


667.4 


548 


1027.9 


0.438 


0.584 


.000580 


0.0589 


536.7 


665.9 


549 


1036.4 


0.434 


0.580 


.000575 


0.0585 


537.8 


664.4 


550 


1045.0 


0.430 


0.575 


.000570 


0.0581 


538.9 


663.0 


560 


1133.9 


0.393 


0.536 


.000522 


0.0542 


550.5 


647.6 


570 


1228.7 


0.358 


0.499 


.000485 


0.0506 


562.1 


631.2 


580 


1329.6 


0.326 


0.465 


.000448 


0.0472 


573.9 


613.3 


590 


1436.9 


0.297 


0.435 


.000415 


0.0440 


585.8 


593.8 


600 


1550.7 


0.27O 


0.407 


.000384 


0.0410 


598.0 


572.4 


610 


1672 


0.245 


0.381 




0.0382 


610.4 


548.8 


620 


1800 


0.221 


0.357 




0.0355 


623.1 


522.3 


630 


1935 


0.199 


0.335 




0.0330 


636.3 


492.4 


640 


2078 


0.178 


0.315 




0.0308 


650.4 


458.2 


650 


2229 


0.157 


0.298 




0.0288 


666.0 


418.6 


660 


2388 


0.137 


0.279 




0.0270 


684 


372 


670 


2556 


0.115 


0.262 




0.0254 


707 


311 


680 


2733 


0.092 


0.248 




0.0239 


740 


229 


689 


2900 


0.049 


0.236 




0.0226 


847 










APPENDIX. 






601 






Principal Steam Table 


Table II. 


8 


9 


10 


11 


12 


13 





H 


I 


K 


o 


b 


N 


t 


1207.6 


615.6 


1122.7 


0.7146 


0.7080 


1.4226 


525 


1207.5 


614.4 


1122.6 


0.7157 


0.7060 


1.4217 


526 


1207.3 


613.2 


1122.5 


0.7168 


0.7040 


1.4208 


527 


1207.2 


612.0 


1122.4 


0.7180 


0.7020 


1.4200 


528 


1207.0 


610.8 


1122.3 


0.7191 


0.7000 


1.4191 


529 


1206.8 


609.6 


1122.2 


0.7203 


0.6979 


1.4182 


530 


1206.7 


608.3 


1122.1 


0.7214 


0.6959 


1.4173 


531 


1206.5 


607.1 


1122.0 


0.7226 


0.6939 


1.4165 


532 


1206.3 


605.9 


1121.8 


0.7237 


0.6919 


1.4156 


533 


1206.1 


604.7 


1121.7 


0.7249 


0.6898 


1.4147 


534 


1205.9 


603.4 


1121.6 


0.7260 


0.6878 


1.4138 


535 


1205.7 


602.2 


1121.4 


0.7271 


0.6858 


1.4129 


536 


1205.5 


600.9 


1121.3 


0.7283 


0.6837 


1.4120 


537 


1205.2 


599.7 


1121.1 


0.7294 


0.6817 


1.4111 


538 


1205.0 


598.4 


1121.0 


0.7305 


0.6796 


1.4101 


539 


1204.8 


597.1 


1120.8 


0.7317 


0.6775 


1.4092 


540 


1204.5 


595.8 


1120.6 


0.7328 


0.6755 


1.4083 


541 


1204.3 


594.5 


1120.4 


0.7340 


0.6734 


1.4074 


542 


1204.0 


593.2 


1120.2 


0.7351 


0.6713 


1.4064 


543 


1203.7 


591.9 


1120.0 


0.7363 


0.6692 


1.4055 


544 


1203.4 


590.6 


1119.8 


0.7374 


0.6671 


1.4045 


545 


1203.2 


589.3 


1119.6 


0.7385 


0.6651 


1.4036 


546 


1202.9 


588.0 


1119.4 


0.7397 


0.6630 


1.4026 


547 


1202.6 


586.7 


1119.2 


0.7408 


0.6609 


1.4017 


548 


1202.2 


585.3 


1118.9 


0.7419 


0.6588 


1.4007 


549 


1201.9 


583.9 


1118.7 


0.7431 


0.6566 


1.3997 


550 


1198.1 


569.9 


1115.7 


0.7545 


0.6352 


1.3897 


560 


1193.3 


554.9 


1111.9 


0.7658 


0.6131 


1.3789 


570 


1187.2 


538.6 


1106.9 


0.7772 


0.5899 


1.3671 


580 


1179.6 


521.0 


1100.6 


0.7886 


0.5657 


1.3543 


590 


1170.4 


501.7 


1092.9 


0.8001 


0.5402 


1.3403 


600 


1159.2 


480.6 


1083.4 


0.8117 


0.5131 


1.3248 


610 


1145.4 


456.9 


1071.7 


0.8235 


0.4838 


1.3073 


620 


1128.7 


430.3 


1057.5 


0.8357 


0.4519 


1.2876 


630 


1108.6 


400.0 


1040.3 


0.8486 


0.4167 


1.2653 


640 


1084.6 


365.1 


1019.9 


0.8627 


0.3772 


1.2399 


650 


1056 


324 


995 


0.879 


0.332 


1.211 


660 


1018 


271 


964 


0.900 


0.275 


1.175 


670 


969 


200 


923 


0.929 


0.201 


1.130 


680 


847 





821 


1.022 


0.0 


1.022 


689 



602 



THE STEAM ENGINE AND TURBINE 





Table III. 


Supplementary Steam Table 







i 


2 


3 


4 


5 


6 


7 


8 


t 


V 


w 


d w 


pw 


ps 


c 


APw 


APu 


32 


0.089 


.01602 


62.42 


0.001 


292.68 


1.0067 


.0002 


54.17 


* 40 


0.122 


.01602 


62.43 


0.002 


297.41 


1.0033 


.0004 


55.05 


50 


0.178 


.01602 


62.42 


0.003 


303.31 


1.0000 


.0005 


56.14 


60 


0.256 


.01603 


62.37 


0.004 


309.20 


0.9977 


.0007 


57.23 


70 


0.363 


.01605 


62.30 


0.006 


315.06 


0.9966 


.0011 


58.31 


80 


0.506 


.01607 


62.21 


0.008 


320.90 


0.9963 


.0015 


59.40 


90 


0.696 


.01610 


62.11 


0.011 


326.72 


0.9964 


.0020 


60.47 


100 


0.946 


.01613 


62.00 


0.015 


332.50 


0.9966 


.0028 


61.54 


110 


1.271 


.01616 


61.86 


0.021 


338.24 


0.9969 


.0039 


62.60 


120 


1.689 


.01620 


61.71 


0.027 


343.94 


0.9974 


.0052 


63.65 


130 


2.219 


.01625 


61.55 


0.036 


349.60 


0.9980 


.0067 


64.70 


140 


2.885 


.01629 


61.38 


0.047 


355.21 


0.9988 


.0087 


65.74 


150 


3.715 


.01634 


61.19 


0.061 


360.76 


0.9996 


.0113 


66.76 


160 


4.74 


.01639 


60.99 


0.078 


366.25 


1.0006 


.0144 


67.78 


170 


5.99 


.01645 


60.79 


0.099 


371.67 


1.0018 


.0183 


68.77 


180 


7.51 


.01651 


60.57 


0.124 i 


377.03 


1.0031 


.0229 


69.76 


190 


9.34 


.01657 


60.35 


0.155 


382.30 


1.0044 


.0285 


70.73 


200 


11.53 


.01663 


60.12 


0.192 


387.49 


1.0059 


.0353 


71.68 


210 


14.12 


.01670 


59.88 


0.236 


392.59 


1.0076 


0.044 


72.62 


220 


17.19 


.01677 


59.63 


0.288 


397 . 60 


1.0093 


0.053 


73.54 


230 


20.78 


.01684 


59.37 


0.350 


402.50 


1.0112 


0.065 


74.43 


240 


24.97 


.01692 


59.11 


0.423 


407.28 


1.0133 


0.078 


75.30 


250 


29.82 


.01700 


58.83 


0.507 


411.92 


1.0151 


0.094 


76.15 


260 


35.42 


.01708 


58.55 


0.605 


416.42 


1.0177 


0.112 


76.96 


270 


41.85 


.01716 


58.26 


0.719 


420.78 


1.0201 


0.133 


77.75 


280 


49.19 


.01725 


57.96 


0.850 


425.00 


1.0226 


0.157 


78.50 


290 


57.34 


.01735 


57.65 


0.999 


429.06 


1.0253 


0.185 


79.23 


300 


66.98 


.01744 


57.33 


1.168 


432.97 


1.0281 


0.216 


79.92 


310 


77.6 


.01754 


57.00 


1.362 


436.71 


1.0310 


0.252 


80.58 


320 


89.6 


.01765 


56.66 


1.581 


440.28 


1.0340 


0.293 


81.20 


330 


103.0 


.01776 


56.31 


1.830 


443.68 


1.0372 


0.339 


81.78 


340 


117.9 


.01788 


55.95 


2.108 


446.90 


1.0405 


0.390 


82.33 


350 


134.5 


.01800 


55.57- 


2.421 


449.93 


1.0439 


0.448 


82.83 


360 


152.9 


.01812 


55.18 


2.77 


452.76 


1.0475 


0.512 


83.29 


370 


173.2 


.01825 


54.78 


3.16 


455.40 


1.0512 


0.585 


83.70 


380 


195.5 


.01839 


54.37 


3.60 


457.82 


1.0550 


0.666 


84.07 


390 


220.1 


.01854 


53.95 


4.08 


460.01 


1.0589 


0.755 


84.38 


400 


246.9 


.01869 


53.52 


4.62 


461.97 


1.0630 


0.855 


84.65 


410 


276.3 


.01884 


53.08 


5.21 


463.67 


1.0672 


0.965 


84.85 


420 


308.3 


.01900 


52.63 


5.86 


465.10 


1.0715 


1.084 


85.00 


430 


343.1 


.01917 


52.17 


6.58 


466.24 


1.0759 


1.216 


85.08 


440 


380.8 


.01935 


51 .70 


7.37 


467.07 


1.0805 


1.363 


85.09 


450 


421.7 


.01953 


51 .'22 


8.23 


467.57 


1.0852 


1.523 


85.02 


460 


465.8 


.01971 


50.74 


9.18 


467.72 


1.0900 


1.699 


84.87 


470 


513.4 


.01990 


50.25 


10.21 


467.50 


1.0950 


1.890 


84.64 


480 


564.6 


.02010 


49.74 


11.33 


466.90 


1 . 1002 


2.098 


84.32 


490 


619.8 


.02031 


49.22 


12.59 


465.88 


1 . 1056 


2.329 


83.90 


500 


679.0 


.02053 


48.68 


13.95 


464.41 


1.1113 


2.582 


83.38 



For definitions and explanations of quantities, see pages 574 to 577. 



APPENDIX. 



603 



Table III — Continued. 






l 


2 


3 


4 


5 


6 


7 


8 


t 


V 


w 


*w 


pw 


ps 


c w 


APw 


APu 


510 


743 


.02077 


48.12 


15.43 


462.5 


1.1175 


2.86 


82.76 


520 


811 


.02103 


47.54 


17.05 


460.1 


1.1244 


3.16 


82.00 


530 


884 


.02131 


46.94 


18.83 


457.2 


1 . 1320 


3.48 


81.13 


540 


962 


.02161 


46.31 


20.77 


453.7 


1.140 


3.84 


80.14 


550 


1045 


.02192 


45.66 


22.89 


449.8 


1.149 


4.23 


79.02, 


560 


1134 


.02224 


44.99 


25.2 


445.3 


1.159 


4.66 


77.75 


570 


1229 


.02257 


44.29 


27.8 


440.0 


1.170 


5.13 


76.31 


580 


1330 


.02294 


43.56 


30.5 


433.9 


1.185 


5.65 


74.67 


590 


1437 


.02339 


42.79 


33.6 


426.9 


1.205 


6.22 


72.82 


600 


1551 


.02383 


41.97 


37.0 


418.9 


1.245 


6.85 


70.67 


610 


1672 


.02434 


41.09 


40.7 


409.4 




7.54 


68.23 


620 


1800 


.02491 


40.14 


44.8 


398.2 




8.29 


65.40 


630 


1935 


.02558 


39.10 


49.5 


385.0 




9.16 


62.09 


640 


2078 


.02635 


37.95 


54.8 


369.2 




10.14 


58.20 


650 


2229 


.02727 


36.67 


60.8 


350.0 




11.26 


53.52 


660 


2388 


.0284 


35.2 


67.8 


326.3 




12.6 


47.8 


670 


2556 


.0299 


33.5 


76.8 


294.2 




14.2 


40.2 


680 


2733 


.0324 


30.9 


90.0 


250.2 




16.7 


29.6 


689 


2900 


.0487 


20.5 


141.3 


141.3 




26.2 






Table IV. Temperature Factor f t for High Range, 
above Column 5 of Table II. See page 72. 



t 


i_ 600 


700 


800 


900 


1000 


1100 


1200 





.0410 


.0212 


.0119 


.0068 


.0034 


.0017 


.0009 


10 


.0382 


.0200 


.0112 


.0064 


.0032 


.0016 


.0009 


20 


.0355 


.0188 


.0106 


.0059 


.0030 


.0015 


.0008 


30 


.0330 


.0177 


.0100 


.0055 


.0028 


.0014 


.0008 


40 


.0308 


.0167 


.0095 


.0052 


.0027 


.0014 


.0007 


50 


.0288 


.0158 


.0090 


.0048 


.0025 


.0013 


.0007 


60 


.0270 


.0149 


.0086 


.0045 


.0023 


.0012 


.0007 


70 


.0254 


.0141 


.0081 


.0042 


.0021 


.0011 


.0006 


80 


.0239 


.0133 


.0077 


.0039 


.0020 


.0010 


.0006 


90 


.0225 


.0126 


.0072 


.0036 


.0018 


.0010 


.0006 


100 


.0212 


.0119 


.0068 


.0034 


.0017 


.0009 


.0005 



Table V. Pressure Factor f P for High Range, above 
Equation (65). See page 72. 



p 


i 


A/ 
P 


V 


4 


a/ p 


V 


i 


A/ 
P 


900 


2.2859 


.0002 


1100 


2.5817 


.0103 


1350 


2.9836 


.0550 


950 


2.3589 


.0018 


1150 


2.6587 


.0158 


1400 


3.0686 


.0686 


1000 


2.4322 


.0036 


1200 


2.7371 


.0228 


1450 


3.155 


.084 


1050 


2.5062 


.0062 


1250 
1300 


2.8174 
2.8991 


.0317 
.0420 


1500 


3.245 


.102 



604 



THE STEAM ENGINE AND TURBINE. 



DEG. 100 Sup 200 
400 . 500 DEG. 




ZOO 300 Dec 400 Temp. 500 600 700 800 

6 OEG. 100 Sup 26a 300 400 500 600 700 



TABLE VI, page A. 



Specific Volume of 



APPENDIX. 



605 



DEC 100 Sup 200 300 400 500 600 700 

600 700 DfcG. 800 TEMP 900 1000 I1QQ 1200 




DtG 100 SUP 200 
Superheated Steam. 



300 



400 



500 600 700 

TABLE VI, page B. 



606 



THE STEAM ENGINE AND TURBINE. 





,^ra 


^§e__L 


-__s==::bL_ 


■ __ ____ L. _[_..]., 



ZOO 




150 1160 h H70 Bt.u 1180 

TABLE VII, page A. 



190 



1200 
Total Heat of 



APPENDIX. 



607 



200 




1200 



1210 h 1220 B.T.U. 1230 



1240 



Superheated Steam. 



Curves. 430 

1250 1260 

Table VII, page B. 



608 



1000 



1200 



THE STEAM ENGINE AND TURBINE. 
1220 1240 1260 1280 



1300 




300 Temp, of 350 IsotH 400 Cv/rves. 
1200 li 1220 B.T.U. 1240 1260 

TABLE VII, page C. 



550 
1280 1300 

Total Heat of 



I00OH 



BIIHllll^iWCI M W 



APPENDIX. 

1340 1360 




800 



600 



500 



400 



550 Temp, or 
1300 1320 h 1340 

Superheated Steam. 



600 Isoth. 650| Curves. "700 \150 

1360 1 380 B.TU 1400 1420 

TABLE VII, page D. 



THE STEAM ENGINE AND TURBINE. 
1450 1500 1550 I 




800 Temp, of |900 Isom | 1 000 Curves. | NOOj 

1500 ' . ' 1550 B.T.U. 160^. 

Total Heat, 



1400 h 1450 
TABLE VII, page E. 



1640 



APPENDIX. 



611 




1.4 n 15 

TABLE VIII, page A. 

Entropy of Superheated Steam. 
Pages A, B, and C run side by side in sequence, pages D and E go above them. 



612 



THE STEAM ENGINE AND TURBINE. 



j3 0, S ? 
1 1 1 1 1 1 1 1 1 1 lii 1 1 li i li 1 1 1 1 1 1 



O (O (Q O 

r> _j <; rsi 



12 — — °° y) in t 

I i I1111I1111I1111I1111I1111I i i i i I i 







TABLE VIII, page B. 




Dec Sat. of 100 \ Const. 80 press. \ so Lines 50 \40 
\\9 ZQ n 21 2.2 

TABLE VIII, page C. 



614 



THE STEAM ENGINE AND TURBINE. 



1000 800 600 400 300 200 150 100 p 60 40 30 25 

' I I i I t 1 i IiiiiIiiiiI 1 1 i i IiiiiIiiiiI i ii i liUi lililil i I i I i lii!iliiiil)i i i Inn 




P.5" J n 

TABLE VIII, page D. 



Entropy op 



APPENDIX. 



615 



30 20 15 

IiiiiIiihIii i i 



10 1 5 p 3 1 1.5 1.0 0.7 0.5 

■ 1 1 1 i 1 ' liiiiliiiil i I i i Innl i I I i hill i I i 1 i I i 



03 02 

i I i 1 




'2.0 n 

Superheated Steam 



2.3 ° ^ 2!4 2'.5 

TABLE VIII, page E. 



616 THE STEAM ENGINE AND TURBINE. 

{From page 579) 
D. Notes on Steam-table Data 

1. The preceding tables will be found to agree quite closely with 
the Marks and Davis Tables of the Properties of Steam. The differences 
lie within the range of variation of the better experimental data; but 
the changes which here appear are in direction of a smoother variation of 
the several quantities. The notes and references which follow do not 
attempt to cover the field of experimental investigation along this line; " 
rather, they touch on a few important points, and may be considered 
as supplementing the " Discussion of Sources " by Marks and Davis. 

2. The pressure-temperature relation follows the determination of 
Holborn and Henning, Annalen der Physik, 1908, Vol. 26, 833-883 — 
see also Heck, Trans. A. S. M. E., 1909, Vol. 30, 345-358. From 212 
deg. to 400 deg. fahr. the values in the table are from the formula 

1 _P_ * p W~ 212 - °- 92563 (689 - ty - 477 4 
§ 14.697 T T 1,000,000,000, ' * W 

in which absolute temperature T = t + 459.4, corresponding with the 

commonly used centigrade value T = t + 273. This modification of 

Thiesen's formula agrees almost perfectly with the experiments. From 

212 deg. down to 32 deg. the values given by Holborn and Henning are 

used directly. Above 400 deg. an interpolation was made among the 

data available in the year 1909; and up to 550 deg. fahr. this has been 

found to agree very closely with the authoritative Holborn-Baumann 

determination, Annalen der Physik, 1910, Vol. 31, 945-970: see also 

L. S. Marks, Jour. A. S. M. E., May 1911, and discussion by Author, 

September, 1911, page 1044. 

3 The differential coefficient dp/dt was calculated from Eq. (a), 

and by the method of supplementary correction where the curve of 

p on t did not follow a formulated equation. This was for use in Clapey- 

ron's equation, 

r _ 144 dp 

u 778 dt' •'■ w 

which connects volume u with latent heat r. 

4. The specific volume of steam (saturated and superheated) is in 
close accord with Linde's equation, of which the experimental founda- 
tion (see Fig. 43 ante) and the evaluation are given in Zeitschrift des 
Vereines deutscher Ingenieure,. 1905, page 1697. His pressure function 
/ p is retained, but the temperature function f t is adjusted so as to make 
soru agree perfectly with r : above the range of Linde's formula (or above 
200 deg. cent.) / t departs more and more from his mathematical ex- 
pression, which becomes of decidedly unsuitable value; and at very 






• APPENDIX. 617 

high temperatures it is very much of a guess, guided by the rational 
requirement that steam shall approach the law pv = CT as it gets 
farther away from saturation. 

5. As to specific heat of water and heat of the liquid, this table 
agrees with that of Marks and Davis in adopting the determination of 
Dieterici, Annalen der Physik, 1905, Vol. 16, 593-620. Above the ex- 
perimental limit of about 600 deg. fahr. the curve in Fig. 45 is pure 
extrapolation, following what seems a probable course, so that the values 
of q are not to be considered at all authoritative. 

6. Up to 400 deg. fahr. the latent heat r is guided by experimental 
values, mostly from electro-calorimetry. Of determinations at and 
below 212 deg., the most convenient summary will be found in an ar- 
ticle by Prof. A. W. Smith, in Physical Review, 1907, Vol. 25, 145-170, 
or better, in Monthly Weather Review for Oct., 1907. Over the range 
from 212 to 400 deg., the later experiments of Henning are published 
in Annalen der Physik, 1909, Vol. 29, 441-465. 

7. For both total heat // and latent heat r the derivation by Dr. 
H. N. Davis from the throttling experiments plotted in Fig. 68 — see 
Trans. A. S. M. E., 1908, Vol. 30, 741-774 — is the real determinant, 
up to the limit of about 400 deg. fahr.* The departure from Davis' 
equation is called for and guided by the need of getting a smooth curve 
for the derivative dH/dt, which in his layout makes a slight but abrupt 
change from constancy to variability at 212 deg. The use of a smaller 
value of r at 212 deg. is based largely on the acceptance of Henning's 
determination at the value which he gives, without the increase of 
about 1.2 B.t.u. which Smith makes because of a supposed difference 
in the fundamental electrical units of measurement — Henning stating 
that this correction is not called for. 

In the high range, above 400 deg., r is carried up with u by Eq. (6); 
the extrapolation is rational in idea and smooth and consistent in form, 
and at 1000 lb. pressure is probably of the degree of correctness named 
in § C above. 

8. The law for total heat of superheated steam represented by the 
simple isothermal curves in Table VII is new, or at least makes promi- 
nent an idea which is only implied in other discussions. This scheme 
of interrelation, combined with experimental data as to the specific 
heat c p , is believed to give a much better determination than can be 
made by experiment alone. The principal data used are those of 
Holborn and Henning (Ann. Phys., 1905, Vol. 18, 739) and of Knob- 

* These throttling experiments have been published as follows: Grindley, Phil. 
Trans. Royal Society, 1900, Vol. 194 A, 1-36: Griessmann, Zeit. Ver. d. Ing., 1903, 
Vol. 47 II, 1852, 1880: Peake, Proceedings Royal Society, 1905, Vol. A 76, 185. 



618 THE STEAM ENGINE AND TURBINE. 

lauch and Jakob (Zeit. Ver. d. Ing., 1907, 81, 121), together with a 
rational derivation of the initial c p , at or against the saturation line — 
see the paper by H. N. Davis, above referred to. 

9. The calculation of internal energy and of entropy are purely 
numerical operations, not involving any combination or interpretation 
of data. 

10. It will be noted that nothing has been said of the great work 
of Regnault in determining the properties of steam, upon which were 
based all the steam tables in use up to a few years ago. The changes 
made by recent experiment are not very great, when expressed in 
percentages, but they are sufficient to. cause the values obtained by 
Regnault to be superseded. 



INDEX 



Absolute Efficiency, 53, 232 

Absolute Pressure, 69 

Absolute Temperature, 38 

Absolute Velocity, in Vane Channel, 451 

Absolute Zero, 38 

Acceleration of Piston, 303, 307 

Accumulator, Rateau, 515 

Accuracy of Steam Calorimetry, 137 

Of Steam Tables, 577 
Action of Clearance Steam, 199 
Action of Cooling Surface, 555 
Action of Entrainment, 537 
Action of Jet upon Vane, 439 

In Multiple-impulse Turbine, 450 
Action of Safety Cams, 408 
Action of Steam in Engine, Chap. V, 
142 

General Description, 15 
Action of Steam in Turbine, Chap. 

IX, 434 
Actual Flow of Steam, 127 
Actual Steam Rates, 231 
Adiabatic Curve of Air, 46 
Adiabatic Curve of Steam, 94 

Effect of Initial Condition, 96 
Adiabatic Expansion, of Air, 45 

Of Steam, 91 

Temperature-entropy Line, 57 
Adiabatic Temperature Range, 46 
Adjustment, by Governor, 426 
Admission, Symmetrical, by Valve, 379 
Admission to Engine Cylinder, 143 
Admission Valves, Corliss, 403, 413 

Lift-valve Gear, 420 

Turbines, 530-534 
Advance, Angle of, 369 
Air and Vapor Mixture, in Condenser: 

Law of Proportion, 547 

Proportions of, 551 

Quantity of Air Present, 552 

Volume of Mixture, 549 
Air-break Pump, Indicator Diagrams, 

424 
Air-compressor Governor, 432 
Air, Thermodynamic Formulas for, 40 
Air Pumps, § 53, 565 

Clearance and Volumetric Efficiency, 
565 



Air Pumps, Edwards Pump, 565 

Leblanc Water Ejector, 567 

Power for Pumps, 568 

Tomlinson Ejector, 568 

Water Ejectors, 566 
Air-pump Capacity, 552, 569 
Allen Valve, 399 

Piston Valve, 400 
Analysis for Thermal Effect, §24, 209 
Angle of Advance, 369 
Appendix, 573 
Area of Steam Jet, 112 

Comparison of Areas, 120 
Argument from Reversibility, 63 
Auxiliaries, Working of, 235 

Power for Condenser Pumps, 568 
Availability of Carnot Cycle, 54, 102 
Availability of Heat, 59 
Average Combined Diagram, 158 

Balanced Valves, 397, 399 
Balancing the Engine, § 34, 334 
Diagrams of Shaking Force, 335 
Effects of Shaking Force, 342 
Forces and Masses Involved, 334 
Radial Resultant Method, 341 
Rod Effect, 340 

Shifting-force Determination, 338 
Side-crank Duplex Engine, 337 
Torque Effect, 339 
Balancing the Turbine Rotor, 520 
Barometric Condenser, 546, 554 
Barrus' Engine Tests, 190, 257 
Batho, Temperature in Steam Jet, 464 
Bearing Pressure, 295 

Diagrams of, 332 
Bearings for Engines, 357 

For Turbines, 520 
Bed and Bearings of Engine, 11, 347 
Behavior of Clearance Steam, 202, 215 
Bilgram Valve Diagram, 371 
Blades for Turbines, 526 
Boiler, Function and General Action, 4 
Borsody and Cairncross, Steam Jet Ex- 
periments, 462 
Boulvin, Compression Tests, 207 
Briling, Jet Impulse Experiments, 472, 
475 



619 



620 



THE STEAM ENGINE AND TURBINE. 



British Thermal Unit, 34 
Buckets, Turbine- wheel, 511 

Action of Jet upon, 442 
Buckeye Shaft Governor, 430 
B Valve, 398 

Callendar and Nicholson Experiments : 

Cylinder-wall Action, 220 

Leakage, 196 
Calorimeter, see Steam Calorimeter 
Carnot Cycle, Availability of, 54, 102 

Reversibility of, 63 

Temperature-Entropy Diagram, 57 

With Gas, 50 

With Steam, 100 
Carpenter, Engine Tests, 184, 249, 262 
Centrifugal Balance, Turbine Rotor, 520 
Centrifugal Force, at Rim of Turbine 
Wheel, 518 

Ideal, in Engine, 308 
Centrifugal Pressure of Jet, 438 
Centrifugal Stress, Fly-wheel, 324 

Turbine Rotor, 519 
Channel, Curved, Flow in, 473 
Channel Form and Area, in Turbine, 448 
Characteristics of Valves, 396 
Clapeyron's Equation, 617 
Classification and Characteristics of 

Engines, § 3, 20 
Classification of Turbines, 32 
Clausius Cycle, see Rankine Cycle 
Clearance and Compression, 146, 199 
Clearance, Filling, 147 
Clearance, in Air Pump, 565 
Clearance Steam, 146, 199 

Action in Expansion, 148 

Behavior of, 202, 210, 215 

Cycle of, 204, 215 

First Approximation, 200 

Real Effect, 201 
Coefficient of Discharge, Steam Flow, 453 
Coefficient of Expansion, of Gas, 39 

Of Steam, 74 
Coefficient of Heat Transfer, Surface Con- 
denser, 557 
Collmann Valve Gear, 420 
Combined Diagrams, Compound Engine, 
155 

Average Diagram, 158 

Combination on Compression Lines ,157 

Examples, 246-262 

Quality Curves, 158, 255 
Combined Efficiency, Engine and Gen- 
erator, 278 
Combined Engine and Turbine Unit, 499 
Combustion, in Boiler Furnace, 1 
Comparison of Jet Areas, 120 
Comparison of Steam Action, Effect of 

Jackets, 254 
Comparison of Steam Diagrams, Actual 

with Ideal, 142 
Complete Valve Diagram, 365 



Compound Engine, § 20, 150 

Arrangement and Working, 152 

Combined Diagrams, 155 

Cylinder Proportions, 290 

Cylinder Ratio, 151, 287 

Equalization of Work Areas, 287 

General Relations, 289 

Lines of Intermediate Pressure, 153 

Separate Diagrams, 151 

Variation of Load, 288 
Compounding, Objects of, 150 
Compressed Steam, Behavior of, 202, 215 
Compression and Clearance, 146, 199 
Compression Curve, Form of, 149 
Compression, Effects of, 199 

Actual Effect, Conclusions, 208 

Engines with Large, 193, 250 

Engines with Small, 247 

Influence upon Expansion, 148, 203 

Tests with Variable, 206 

See also Clearance Steam 
Condensate, Removal of, 546 

Volume of, 549 
Condensation by Cylinder Walls, 225 

See Cylinder Condensation 
Condensation, 4, 545 

Action of Cooling Surface, 555 

Air and Vapor Mixture, 549 

Efficiency of Cooling Surface, 562 

Heat Transfer in, 557 

Principle of, 545 

Quantity of Air, 552 

Removal of Condensate, 546 
Condenser Pumps, see Air Pumps 
Condensers, and Air Pumps, § 53, 545 

Barometric Condenser, 546, 554 

Contraflo, 563 

Countercurrent, 553, 564 

Leblanc, 567 

Parsons Vacuum Augmenter, 564 

Performance, Surface Type, 558 

Self-cooling, 569 

Simple Jet Condenser, 546 

Simple Surface Condenser, 547 

Tomlinson, 555 

Tube Joint, 547 

Types of Condenser, 545 

Wheeler Dry-tube, 563 
Connecting Rod, 10 

Construction of, 354 

Effect on Shaking Force, 340 

Exact Force Action, 294 
Constant Steam Weight, Curve of, 97 
Constants for Engine, 161 
Constrained Motion, 298 
Construction and Working of En- 
gine, § 2, 5 
Construction of Engine, § 36, 343 

Bearings, 357 

Connecting Rod, 354 

Crank Shaft, 356 

Crosshead, 351 



INDEX. 



621 



Construction of Engine, Cylinder, 343 

Framework, 347 

Piston, 348 

Piston Rod and Packing, 350 

Steam Jackets, 347 

Stuffing Boxes, 350 

Support of Cylinder, 347 

Valve Chest and Steam Passages, 347 

Wheels, 358 
Construction of Working Parts (Tur- 
bine), § 51, 516 
Continuous Throttling, 129 
Contraflo Condenser, 563 
Control of Regulation, Engine Governor, 

431 
Conversion of Heat, Efficiency in, 59 
Cooling Surface, Action of, 555 

Efficiency of, 562 
Cooling Tower, 568 
Corliss Valve Gear, § 43, 403 

Cut-off Action, 411 

Cut-off Gear, 405 

Dashpot, 416 

Eccentric Setting and Valve Action, 
410 

Forms of Valve, 404, 413 

Gear on Cylinder, 405 

Governor, 406 

Indicator Diagrams, 412 

Two Eccentrics, 415 

Valve Diagrams, 411 

Valve Movement, 409 

Valve Hesistance, 413 

Valve Setting, 412 
Counterbalancing, see Balancing En- 
gine 
Countercurrent Condensers, 553, 564 
Crank Shaft and Wheels, 11, 356, 358 
Crank Shaft, Engine without, 421 
Cross Area of Steam Jet, 112 
Crosshead Construction, 351 
Curtis Turbine, 27 

Blading, 527 

Governor and Valves, 533 

Pivot Bearing, 522 
Curved Channels, Flow in, 473 
Curves of Pressure Variation in Jet, 460 
Curves of Steam Consumption, 170 
Cut-off Control, Turbine, 533 
Cut-off Gear, Lift-valve Engine, 420 
Cut-off, Ratios of, 144 
Cut-off Valve, Functions of, 392 
Cut-off, Variable, see Variable Cut-off 
Cut-off, Variation of Missing Steam with, 
180 

Influence of Variation, 185 
Cycle, Carnot, with Gas, 50 

Carnot, with Steam, 100 

Dynamic-force, 23, 111 

Irreversible, 62 

Rankine, 104 

Regenerative, 110 



Cycle, Reversible, 63 

Static-pressure, 22, 100 

Steam-engine, 106 

Thermodynamic, General, 49 
Cycle of Clearance Steam, 204 
Cycle of Steam Jet, 131 

Heat Waste in, 132 
Cylinder and Valve Chest, 12 
Cylinder Condensation, Formula for, 175 

Effect of Speed, 187 

Effect of Throttling, 186 

Influence of Size, 195 

Range of Temperature, 189, 191 

Value of Formula, 196 

Variation with Cut-off, 180 
Cylinder Constants, 161 
Cylinder Construction, 343 

Corliss, 404 

Lift-valve, 346 
Cylinder, Proportioning for Power, 281 
Cylinder Ratio, 151, 286, 290 
Cylinder Walls, Effect of, 175, 209 
Cylinder Walls, Thermal Action of: 

Calculation of Heat Absorbed, 221, 223 

Conclusions, 229 

Experiments, 219 

Influence of Speed, 222 

Information Available, 218 

Rate of Condensation, 225 

Rate of Heat Absorption, 224 

Steam-temperature Cycle, 219 

Dashpot, Corliss Gear, 416 

Fly-ball Governor, 406 
Dash-relief Valve, 423 
Dean, Pumping-engine Test, 248 
Deflection of Steam Jet, 437 
De Laval Turbine, 24 

Blading, 526 

Governor and Valve, 529 

Nozzle, 524, 534 
Denton and Jacobus, Engine Tests, 170, 

172, 187, 188 
Design and Construction of Tur- 
bine, Chap. X, 503 
Design for Steam Action (Turbine), 
§ 49, 503 

See Turbine Design 
Design of Steam Passages, 400 
Design of Engine Cylinders, 281 
Determining Tangential Force, 315 
Diagram Factor, 281 
Diagram for Throttling Calorimeter, 135 
Diagram, Ideal for Steam Engine, 107 
Diagram, Mollier, 138 
Diagram of Bearing Pressures, 332 

Of Effective Driving Force, 311 

Of Heat Distribution, Sankey, 273 

Of Inertia Force, 308 

Of Pin Pressures, 328 

Of Piston Acceleration, 307 

Of Piston Velocity, 306 



622 



THE STEAM ENGINE AND TURBINE. 



Diagram of Turning Force, 317, 323 
Temperature-entropy, for Engine, 108, 

212 
Temperature-entropy, for Plant, 274 
Diagrams, Combined, Compound En- 
gine, 155 
Diagrams of Corliss Valve Movement, 
410 
Of Plant Performance, 272 
Of Properties of Superheated Steam, 

604-615 
Of Shaking Force, 335 
Of Steam Consumption, 170 
Of Steam Velocity in Turbine, 439-451 
Of Valve Movement, 363 
Directions of Steam Flow, in Turbine, 

510 
Discharge, Coefficient of, 453 
Disc Wheels, Turbine, 517 
Disgregation Work, 41 
Double-tube Injector, 540 
Double-valve Gear, § 41, 391 
Relative Movement, 392 
Varying Cut-off, 394 
Driving Force on Vanes, 440 
Drum Rotors, 518 
Duchesne Experiments, Temperature in 

Cylinder, 226 
Duplex Pump, 421 
Duty of Pumping Engines, 239 
Dwelshauvers-Dery, Compression Tests, 

202 
Dynamic-force Cycle, § 16, 111, also 

23 
Dynamics of Jet Action, § 46, 434 

Eccentric and Strap, 401 
Eccentric, Equivalent, 386, 388 

Shifting, 376 

Virtual, 392 
Eccentric Locus: 

Radial Gears, 388 

Stephenson Link Motion, 386 

Shaft Governor, 377, 395 
Eccentric Pendulum, 376 
Eccentric Setting, Corliss Gear, 410, 415 

With Negative Valve, 393 
Eccentrics, Use of Two, 415 
Economical Vacuum, 243 
Edwards Air Pump, 565 
Effect of Cylinder Walls, § 22, 175 
Effect of Jackets and Reheaters, 184, 257 

Of Superheating, in Engine, 258 
Effects of Heat, 41 
Effects of Compression, § 23, 199 
Effects of Shaking Force, 342 
Effective Cut-off, 144 
Effective Expansion in Engine, 149 
Effective Radius of Fly Wheel, 322 
Effective Steam Pressure and Driving 

Force, 311 
Efficiencies, Various, of Plant, 234 



Efficiency: 

Absolute and Relative, 53, 232 

Calculation of, for Plant, 236 

Combined, of Engine and Generator, 
278 

In Conversion of Heat, 59 

Mechanical, 275, see also Friction 

Of Air Pump, Volumetric, 565 

Of Cooling Surface, 562 

Of Ideal Engine, 52 

Relative, Discussed, 240 

Thermodynamic, 232 
Efficiency of Jet Formation, 464 

By Condition of Jet, 470 

By Reaction, 466, 468 

Results, 471 
Elektra Turbine, 510 
Energy, External, of Water, 83 

Internal, of Gas, 41 

Internal, of Steam, 82 

Internal, of Superheated Steam, 87 
Energy Losses in Turbine, 477, 494, 502 
Energy of Steam Jet, 112 
Energy Transformed in Throttling, 130 
Engine and Turbine Unit, Performance, 

499 
Engine Bed and Bearings, 11, 347 

Forces on, 296 
Engine Cylinder, Proportioning of, 281 
Engine Layout, 21 
Engine Mechanism, Action of, 5 

Motion of, 298 
Engine Speed, 22 
Engine Tests: 

Barrus, Various, 190, 257 

Boulvin, Compression, 207 

Callender and Nicholson, 196, 220 

Carpenter, Laboratory Engine, 184, 
189 
Pumping Engines, 249, 262 

Dean, Pumping Engine, 248 

Denton and Jacobus, Air Compressor, 
170, 187 

Dwelshauvers-Dery, Compression, 202 

Goss, Pumping Engine, 249 

Isherwood, S. S. Michigan, 181 

Jacobus, Compound Corliss, 174 
High Superheat, 261 

Klemperer, Compression, 206 

Locomotives, Diagrams, 250 

Marine Engines, 253 

Marks, Generator Engines, 183, 186 

Peabody, Small Corliss, 182 

Pennsylvania Railroad, Locomotives, 
190, 194, 250 

Pumping Engines, Diagrams, 247 

Steam Consumption and Missing 
Quantity, 179-199 

Stott, Big Corliss, 256, 489, 499 
• Table 13, 263-271 
Engines with Large Compression, 193, 
250 



INDEX. 



623 



Engines with Small Compression, 247 
Engine without Crank Shaft, 421 
Entrainment by Jet, 537 
Entropy, Idea of, 55 
Entropy of Steam, 88 

Diagram for Steam, 89, 611 
Entropy-temperature Diagram, see Tem- 
perature-entropy 
Equalization of Work Areas, 287 
Equilateral Hyperbola, Construction, 40 

As Steam Curve, 97 
Equivalent Steam Rates, 244 
Evaporation, in Boiler, 3 
Examples of Performance (Engine), 

§ 27, 244 
Exhaust, on Indicator Diagram, 146 
Exhaust Valves, Corliss, 414 
Expansion, Adiabatic, of Air, 45, 

Of Steam, 91 
Expansion, a General Law of, 45 
Expansion at Constant Pressure, Air, 42, 

Steam, 74 
Expansion, Coefficient of, Air, 39 

Steam, 74 
Expansion, Effective, in Engine, 149 
Expansion, Incomplete, in Engine, 108 
Expansion in Engine Cylinder, 145 
Expansion, Influence of Compression 

upon, 203 
Expansion, Isothermal, Air, 44 

Steam, 78 
Experiments on Steam Jet, § 47, 452 

See Steam Jet, Experiments upon 
External Energy of Water, 83 
External Work, 41 

Calculation of, 44 

Of Steam, or of Vaporization, 82 

Fall of Temperature in Throttling, 132 

Feed-water Data, 235 

Feed-water Heater, Function of, 4, 233 

Feed Water, Heat in, 233 

Feed Pump, Function of, 4 

Work of, 83 
Feed Temperature, Ideal, 234 
Filling Clearance Space, 147 
Flow in Curved Channels, 473 
Flow in Turbine, Directions of, 510 
Flow of Steam, 125 

Influences Modifying, 127 

Of Water, 126 
Flow of Steam through Orifices and Noz- 
zles, Experimental, 452-459; see 
also Steam Jet, Experiments upon 
Fly-wheel Action, § 33, 321 

Data from Turning-force Diagram, 318 

Effective Radius, 322 

Multiple-crank Arrangements, 323 

Weight of Wheel, 321 
Fly-wheel Construction, 358 
Foot Pound, 34 
Form of Steam Jet, 113 



Form of the Compression Curve, 149 
Formula for Cylinder Condensation, 175 

Value of, 179, 196 
Formulas, Thermodynamic, for Air, 40 
Force Action, Typical, in Governor, 426 

In Shaft Governor, 429 
Forces in Engine: 

Counterbalancing, 297, 334 

Equilibrium of Shaft, 294, 332 

Exact Action on Connecting Rod, 294 

Forces on Bed, 296 

Mean Turning Force, 293 

On Piston Slide, 291, 311 

Transmission to Crank, 292, 313 

See also Working Forces in Engine 
Forces in the Machine, § 30, 291 
Framework of Engine, 347 
Frictional M.E.P., 280 
Friction and Machine Efficiency, 
§ 28, 275 

Combined Efficiency, 278 

Examples of Performance, 277 

Locomotive Data, 279 

Typical Relations, 277 
Friction by Force Analysis, 280 
Friction Load and Power, 276 
Friction of Steam, 477, 494 
Fullager Balancing System, 513 
Function of Members of Plant, 1 

Separation of, in Actual Plant, 103 
Functions of Cut-off Valve, 392 

Of Governor, 426 

Gaseous Mixture, Law of, 548 

Gas, Perfect, 35 

Gay Lussac, Law of, 36 

Geared Turbine, 516 

Generation and Properties of Steam, 

§ 11, 66 
General Principles of Heat Engine, 

§ 10, 58 
General Thermodynamic Ideas, 33, 49-, 

58 
Goss, Test of Pumping Engine, 249 
Governing the Engine, 18, 426 
Governing the Turbine, see Turbine Gov- 
erning 
Governor Action in Turbine, 535 
Governor, Fly-ball, 406 
Governor, Shaft Type, 19, 376, 430 
Governor, Throttling, 432 
Governors: 

Action in Adjustment, 427 

Control of Regulation, 431 

Examples of Shaft Type, 430 

Force Action, Shaft Type, 429 

Functions of, 426 

Regulation bv Fly-ball, 427 

Stability, 427 

Typical Force Action, 426 
Griessmann, Throttling Experiments, 
133 



624 



THE STEAM ENGINE AND TURBINE. 



Grindley, Throttling Experiments, 133 
Guide-bar Pressures, 331 
Gutermuth, Steam-flow Experiments, 
457 

Harmonic Motion, 298 

Of Slide Valve, 362 
Harter, Flow of Superheated Steam, 456 
Heat Absorbed by Cylinder Walls, 221, 

224 
Heat and Work, § 5, 33 
Heat Consumption per Power Unit, 238 
Heat Distribution, Sankey Diagram, 273 
Heat in Feed Water, 233 
Heat Transfer, in Condenser, 557 
Heat, 33 

Effects of, 41 

Intensity of, 34 

Latent, 80 

Of Formation of Steam, 81 

Of the Liquid, 80 

Of Vaporization, 80 

Quantity of, 34 

Residual, in Exhaust, 60 

Sensible, 33 

Specific, see Specific Heat 

Total of Steam, 80, 85 
Heat Engine, Theory of, Chap. II, 33 

General Principles of, 58 

The Ideal, 49 
Heating, Constant Pressure, 36, 42, 74 

Constant Volume, 36,. 76 

Temperature-entropy Curves, 57 
High Superheat, Performance with, 260 

See also Turbine Performance 
Hirn's Analysis, 210 
Horse Power, Defined, 34 
Horse Power and Steam Consump- 
tion, § 21, 159 
Hydraulic Analogy, 60 
Hyperbola, see Equilateral Hyperbola 

Ideal Action of Steam Jet, see Steam 

Jet 
Ideal Centrifugal Force, in Engine, 308 
Ideal Diagram and Diagram Factor, 281 
Ideal Feed Temperature, 234 
Ideal Heat Engine, § 8, 49 

Efficiency of, 52 
Ideal Steam Cycles, Chap. IV, 100 
Ideal Steam Diagram, 107 

Comparison with Actual, 142 
Ideal Volume of Steam, 71 
Idea of Entropy, 55 

Of Reversibility, 61 
Impulse and Reaction: 

Of Jet, 435 

Meaning and Distinction, 23, 441 
Impulse of Jet, from Vanes, 435, 475 
Impulse Turbine, Variations of, 512 
Impulse upon Jet, 434 
Impulse upon Vanes, Experiments, 475 



Incomplete Expansion, 108 
Increase of Radial Depth, Steam Chan- 
nel, 473 
Indicated Horse Power, 161 

Cylinder Constants, 161 

Mean Effective Pressure, 159 
Indicated Steam Consumption, 165 

Compound-engine Diagrams, 167 
Indicator Diagram, § 19, 142 
Indicator Diagram, 15 

Admission, 143 

Clearance and Compression, 146 

Combined, Compound Engine, 155 

Comparison with Ideal Diagram, 142 

Cut-off, 144 

Expansion Curve, 145 

Information from, 149 

Mean Effective Pressure, 159 

Reference Lines, 142 

Release and Exhaust, 146 
Indicator Diagrams: 

Air-brake Pump, 424 

Compound Engines, 154, 246-262 

Corliss Gear, 412 

Locomotives, 250, 387 

Shaft-governor Engines, 154, 163, 380 

Steam Pumps, 424 
Indicator, Form and Action, 14 
Induced Flow, Divergent Nozzle, 462 
Inertia Force of Reciprocating Parts, 308 

See Balancing Engine 
Infinite Connecting Rod, 302 
Information from Indicator Diagram, 

149 
Injector, 539 

Double-tube, 540 

Performance of, 543 

Range of Working, 544 

Theory of, 541 
Instantaneous Center, 304 
Internal Work or Energy, 41 

Of Steam, 82, 87 

Specific Heat for, 43 
Irreversible Cycle, 62 
Isentropic Expansion, 57, 91 
Isothermal Expansion, 44 

Of Steam, 78, 86 

Temperature-entropy Line, 57 

Jacobus, Engine Tests, 174, 261 
Jet or Jet Action, see Steam Jet 
Jet Condenser, 545, 553 
Joy Valve Gear, 390 

Kerr Turbine, 511 
Kinetic Losses, Engine, 147 
Kinetic Pressure Lowering, 128 
Klemperer, Compression Tests, 206 

Labyrinth Packing, 524 
Latent Heat, 80 
Law of Expansion, 45 






INDEX. 



625 



Law of Gaseous Mixtures, 548 

Of Gases, 36 

Of Gay Lussac, 36 

Of Mariotte, 39 
Laws of Thermodynamics, 64 
Layout of Engine, 21 
Lead, Influence of, 381" 
Leakage, in Engine, 197 
Lift-valve Engine, 417 

Cut-off Gear, 420 

Cylinder, 346 

Valve Gear and Valves, 418 
Limit of Speed, for Wheel, 326 
Linde, Steam-volume Experiments, 77 
Link Motion, Stephenson, 382 
Load and Output, Types of, 275 
Load Factor, Influence of, in Turbines, 

488 
Locomotive Efficiency, Mechanical, 279 
Locomotive Tests, Pennsylvania Rail- 
road, 190, 194 

Steam Diagrams, 250 
Locus of Eccentric Center, 377, 386, 388, 

395 
Locus of Stage Points, Mollier Diagram, 

507 
Losses, Kinetic, in Engine, 147 
Losses of Energy, in Turbine: 

See Turbine Losses 
Low-pressure Turbine, 499, 515 

Rateau Accumulator, 515 
Lubrication of Engine, 12 

Mariotte's Law, 39 
Marine Engine Tests, 253 
Marine Turbine, 515 
Marks, Engine Tests, 183, 186 
Mean Effective Pressure, 159 

Frictional, 280 
Mean Turning Force, 293 
Measurement of Pressure, 69 
Measurement of Steam Consumed, 169 
Measures of Performance, § 26, 231 
Mechanical Efficiency, see Friction 
Melms-Pfenninger Turbine, 512 
Metallic Packing, 351 
Meyer Valve Gear, 391 
Michigan Engine Tests, 181 
Missing Steam Quantity, see Cylinder 

Condensation 
Mixed-type Turbines, 31 
Mollier Diagram, Layout, 138 

Form of the Diagram, 508 

Stage-point Locus, 507 

Use in Turbine Design, 506 

Use in Turbine Tests, 496 
Motion, Constrained, 298 

Harmonic, 298 
Motion of the Engine Mechanism, 
§ 31, 298 

Analytical Derivation, 300, 303 

Diagram of Piston Acceleration, 307 



Motion of the Engine Mechanism, 
Diagram of Piston Velocity, 306 
Graphical Relations, 304 
Infinite Connecting Rod, 302 
Piston Movement, 301 
Velocity and Acceleration, 303 

Multiple-admission Valves, 399 
Corliss, 414 

Multiple-crank Arrangements, 323 

Multiple-expansion Engine, see Com- 
pound Engine. 

Multiple-expansion Turbine, 25 

Multiple-impulse Turbine, 27 
Action of Steam in, 450 

Multistage Turbine, Design of, 508 

Napier Divisor, 120, 125, 453 • 
Negative Valves, 393 

Eccentric Setting for, 393 

In Corliss Gear, 415 
Notes on Steam-table Data, 577 
Nozzles and Distributors, 524 
Nozzles, Flow through, 457 

Induced Flow, 462 

Orifices, Flow of Steam through, 452 

Packing, Engine, 350 

Turbine, 522 
Parsons Turbine, 29 

Blading, 528 

Governor and Valve, 531 
Parsons Vacuum Augmenter, 564 
Partial Vaporization, Heat of, 81 

Volume in, 70 
Path of Jet, in Turbine Vane, 451 
Peabody, Engine Tests, 182 

Steam-flow Experiments, 452 
Peake, Throttling Experiments, 133 
Pennsylvania Railroad Locomotive Tests, 

190, 194, 251 
Perfect Gas, The, § 6, 35 

Laws of, 36 
Performance and Efficiency of the 

Engine, Chap. VI, 231 
Performance of Engines, Examples of, 
244 

Of Injector, 543 

Of Plant, Diagrams of, 272 

Of Steam Blower, 538 

Of Surface Condenser, 558 

With High Superheat, 259 
Perpetual Motion, 61, 65 
Pins and Bearings, Pressures on, 327 
Piston Acceleration, 307 

Construction, 8, 348, 350 

Movement, 301 

Speed, 22 

Velocity, 306 
Piston-lift Valves, 419 
Piston Valves, 398 
Pivot Bearing, Curtis Turbine, 522 






626 



THE STEAM ENGINE AND TURBINE. 



Plant Efficiency, Calculation of, 236 

Plant Performance, Diagrams of, 272 

Poppet Valves, 418 

Ports, Steam and Exhaust, 13, 347 

Positive and Negative Valves, 393 

Power for Condenser Pumps, 568 

Power-unit Ratios, 231 

Pressure and Volume of Steam, § 12, 

67 
Pressure, Constant, with Gas, 36, 42 

With Steam, 74 
Pressure in Jet, Measurement of, 460 

In Curved Channel, 473 
Pressure Lowering, by Throttling, 128 
Pressure, Mean Effective, 159 
Pressure, Measurement of, 69 
Pressures on Pins and Bearings, § 34, 
327 

Approximate, on Pins, 327, 329 

Diagrams of, 328-330 

Guide-bar Pressures, 331 
Pressure Range, Influence in Turbine, 

490 
Pressure-temperature Relation, 67, 578 
Pressure-unit Ratios, 69 
Pressure-volume Measure of Work, 43 
Pressure-volume Product, 71 
Principle of Condensation, 545 
Properties of Steam, Chap. Ill, 66, 
also Appendix, 573 

Pressure and Volume, 67 

Tables and Diagrams, 578-615 

Thermal Quantities, 79 
Proportioning Engine Cylinders, § 29, 

281 
Proportioning the Valve, 401 
Proportions of Air and Vapor Mixture, 

549 
Proportions of Turbine Stages, 508 
Pumping Engines, Duty, 239 

Tests, Diagrams, 248, 262 

Quality Curves, Steam Diagrams, 159, 

255 
Quality of Steam, as to Moisture, 81 
Change of, along Equilateral Hyper- 
bola, 98 
Change of, in Adiabatic Expansion, 93 
Effect on Jet, 122 
Quantity of Air in Condenser, 552 

Radial Valve Gears, 388 

Range of Working of Injector, 544 

Range of Throttling Calorimeter, 136 

Rankine Cycle, 104 

Rateau Accumulator, 515 

Rateau, Experiments on Steam Flow, 453 

Rateau Turbine, 25 

Blading, 527 
Reaction, in Turbine, Meaning, 23, 442 
Reaction of Jet, 435 

Experiments, 465, 466 



Reaction Turbine, 28 

Variations of, 513 
Reaction Wheel, 23 

Efficiency of, 445 
Regenerative Cycle, 110 

Test of Engine, 261 
Regulation by Governor, 427 

Control of, 431 
Reheaters, 173, 257 
Relative Efficiency, 53, 240 

Simple Standard for, 242 
Relative Movement of Cut-off Valve, 392 
Release and Exhaust, 146 
Releasing Valve Gears: 

Corliss, 403 

Gridiron Valves, 417 

Lift Valves, 420 
Removal of Condensate, 546 
Residual Energy, Steam Current, 446, 477 
Residual Heat, in Exhaust, 60 
Reuleaux Valve Diagram, 363 
Reversible Cycle, 63 
Reversibility, Argument from, 63 

Idea of, 61 

Of Process, 62 

Of Steam-jet Cycle, 131 
Reversing Valve Gears, § 40, 382 

Radial Gears, 388 

Stephenson Link Motion, 382 
Riedler-Stumpf Turbine, 511 
Rites Engine Governor, 430 
Robb-Armstrong Governor, 430 
Rocker Arm, 371, 402 
Rolling-mill Reversing Gear, 425 
Rosenhain, Reaction Tests, 465 
Rotary Engine, § 54, 570 
Rotors of Turbines, 516 

Disc Wheels, 517 

Drum Rotors, 518 

Safety Cams, Corliss Gear, 408 

Sankey Diagram, Heat Distribution, 273 

Saturation Line, 71 

Search Tube, Use of, 460 

Self-centering Valve, 425 

Self-cooling Condenser, 569 

Separation of Function, Heat-engine 

Plant, 103 
Separator Calorimeter, 137 
Shaft, see Crank Shaft. 

Forces on, 294 
Shaft Governor, 19 

Examples of, 430 

Force Action, 429 

Shifting Eccentric and Valve Action, 
376 
Shaking Force, see Balancing Engine 

Effects of, 242 
Shifting Eccentric, § 38, 376 

Indicator Diagrams, 380 

Link Motion, 386 

Valve Diagrams, 378 



INDEX. 



627 



Sibley and Kemble, Flow Tests, 458 

Reaction Tests, Steam Nozzle, 466 
Similarity of Steam Jets, 118 
Simple Slide Valve, § 37, 362 
Simple Thermodynamic Operations 

with Gases, § 7, 41 
Single-expansion Turbine, 23, 495 
Size and Speed of Engine, 284 
Size of Engine, Influence of, 195 

Of Turbine, Influence of, 487 
Slide Valves and Gears, Details of, 

§ 42, 396 
Special Graphical Methods, § 18, 138 
Specific Heat: 

For Internal Work, 43 ' 

Of Gas, 42 

Of Superheated Steam, Constant Pres- 
sure, 84; Constant Volume, 87 

Of Water, 79 
Specific Volume and Density, Steam, 70 

Of Superheated Steam, 604 
Speed, Effect on Wall Action, 187, 222 

Influence on Turbine Performance, 494 

Of Engine and Piston, 22 

Of Vane, Variation in, 447 

Of Wheel, Safe Limit, 326 
Stability, of Governor, 427 
Stages, Performance by, 495 
Static Pressure Cycle, § 15, 100, also 

22 
Steam Action, in Engine, 15, Chap. V, 
142-230 

In Engine and Turbine, 22 

In Turbine, 32, Chap. IX, 434-502 
Steam-actuated Valves, 423 
Steam, Adiabatic Curve, 94 

Adiabatic Expansion, 91 

Carnot Cycle with, 100 

Characteristic Equation, 72 

Entropy Diagram, 89, 611 

Entropy of, 88 

Equilateral Hyperbola with, 97 

Expansion under Constant Pressure, 74 

External Work or Energy, 82 

Flow of, 125 

Generation and Properties of, 66 

Heat Curves, 82 

Heating at Constant Volume, 76 

Heat of Formation, 81 

Ideal Volume of, 71 

Internal Energy of, 82, 87 

Isothermal Curve, 78, 86 

Latent Heat, 80 

Pressure-temperature Relation, 67 

Specific Heat, 84, 87 

Specific Volume and Density, 70 

Superheated, 72, 84, 604-615 

Thermal Properties, 79 

Total Heat, 80, 85, 606 

Volume of Superheated, 72, 604 

Working and Clearance, 146 

Work per Pound of, 109 



Steam Blowers, 537 

Steam Calorimeters, 134-138 

Accuracy of, 137 

Diagram for (Throttling), 135 

Range of (Throttling), 136 

Separating, 137 
^ Throttling, 134 
Steam Channel, Dimensions of, 503 

Form and Cross Area, 448 

Increase of Radial Depth, 473 

Path of Jet in, 451 

Proportions of, 509 

Velocity of Jet in, 451 
Steam Condition, Influence on Turbine 

Performance, 490 
Steam Consumption: 

Actual Rates, 231 

Curves of, 170 

Diagram of Specific, 171 

Equivalent Rates, 244 

Indicated, 165 

Measurement of Actual, 169 

Power-unit Ratios of, 231 

Various Steam Quantities, 173 
Steam Current, see Steam Jet 
Steam Diagram, Ideal, 107 

See also Indicator Diagram, 

Unit Diagram, 174 
Steam Diagrams from Various Tests, 
246-262 

Scheme of, 245 
Steam-engine Governors, § 45, 426 

See Governors 
Steam-engine Cycle, 106, 138 
Steam-engine Indicator, 14 
Steam-engine Plant, Outline, 1 
Steam Flow, Directions^of (Turbine), 510 
Steam Jackets, Comparisons, 254 

Construction of, 347 

Effect of, 184, 257 
Steam-jet Apparatus, § 52, 537 
Steam Jet: 

Comparison of Areas, 120 

Cross Area of, 112 

Effect of Initial Conditions, 122 

Efficiency, see Efficiency of Jet 

Efficiency in Formation, 464 

Energy of, 112 

Flow Rates, 125 

Form of, 113 

General Conditions, 111 

Heat Waste in Cycle, 132 

Napier Divisor, 120 

Principal Influences on Form, 124 

Reversibility of Cycle, 131 

Similarity of, 118 

Tables for, 114 
Steam Jet, Experiments upon: 

Batho, Temperature in Jet, 464 

Borsody and Cairncross, Temperature 
in Jet, 462 

Briling, Impulse of Jet, 472, 475 



628 



THE STEAM ENGINE AND TURBINE. 



Steam Jet, Experiments upon: 
Calculation of Efficiency, 468, 470 
Divergent Nozzles, Flow through, 457 
Efficiency in Formation, 464 
Efficiency Results, 471 
Energy Losses, 477, 494, 502 
Flow in Curved Channels, 473 
Flow through Orifices and Nozzles, 

452-459 
Gutermuth, Flow Rates, 457 
Harter, Flow, Superheated, 456 
Impulse of Jet, 464, 475 
Impulse upon Vanes, 475 
Induced Flow, Nozzle, 457, 462 
Peabody, Flow Rates, 452 
Pressure in Jet, 460 
Rateau, Flow Tests, 453 
Rosenhain, Reaction Tests, 465 
Search Tube, Use of, 460 
Sibley and Kemble, Flow, 458; Reac- 
tion, 466 
Stodola, Pressure Curves, 460 
Superheated Steam, Flow, 456 
Temperature in Jet, 462 
Thomas, Impulse Data, 475 ] 
Steam Jet, Ideal Action of: 
Absolute Velocity of Jet, 451 
Action of Jet upon Vane, 439 
Centrifugal Pressure on Vane, 438 
Channel Form and Cross Area, 448 
Deflection of Jet, 437 
Driving Force on Vane, 440 
Impulse and Reaction of Jet, 435 
Impulse upon Jet, 434 
In Multiple-impulse Turbine, 450 
Path of Jet, 451 
Reaction Wheel, 445 
Types of Vane Action, 441 
Vane Form and Speed Change, 447 
Work on Vanes, 443 
Steam Jet, Real Action of: 
Efficiency, 464, 468 
In Curved Channels, 473 
See Steam Jet, Experiments upon 
Steam Passages, Design of, 400 
Steam-power Plant, The, § 1, 1 
Steam-pump Valve Gears, 421 
Steam Rate, see Steam Consumption 
Steam Tables and Diagrams, 578-615 
Accuracy of, 577 
Notes on Data, 616 
Steam-temperature Cycle, 219 
Steam Turbine, The, § 4, 22 
Steam Weight, Curve of Constant, 97 
Stephenson Link Motion, 382 
Arrangement of Rods, 385 
Eccentric Locus, 386 
Movement of Valve, 385 
Stodola, Flow in Curved Channels, 473 
Impulse upon Vanes, 475 
Pressure Curves, Steam Jet, 460 
Stott, Engine Tests, 256, 489 



Stott, Engine and Turbine Tests, 499 
Stress in Rim of Wheel, 324 
Stuffing Box, Construction, 350 

For Turbines, 522 
Sulzer Turbine, 31 

Details, 525, 526 
Sundry Steam Appliances, Chap. XI, 

537 
Superheated Steam, 66 

Entropy of, 611 

Specific Heat of, 84, 87 

Total Heat of, 85, 606 

Volume of, 72, 604 
Superheating, Effect in Engine, 258 

Effect in Turbine, 491 
Surface Condensers, 547, 562 

Performance of, 558 
Surface, Cooling, see Cooling Surface 
Symbols for Steam Quantities, 574 

Tables of Engine Tests, 268-271 

Of Properties of Steam, Appendix, 
578-615 

Of Turbine Performance, 478-485 

See Contents, page ix 
Temperature-entropy Analysis, § 9, 

55 
Temperature-entropy Diagram, 57 

For Engine, 108, 212, 217 

For Plant, 274 

For Turbine, 496 

Utility of (Engine), 215 
Temperature Fall, in Throttling, 132 
Temperature, Ideal, of Feed Water, 234 

In Cylinder, 226 

In Cylinder Walls, 221 

In Steam Jet, 462 
Temperature Limits in Heat Engine, 49 
Temperature Range and Cylinder Ac- 
tion, 189 
Test of Injector, 543 
Tests of Engines, see Engine Tests 
Tests of Turbines, see Turbine Perform- 
ance 
Tests with Variable Compression, 206 
Theory of Heat Engine, Chap. II, 33 
Theory of Injector, 541 
Thermal Action of Cylinder Walls, 

s 05 218 
Thermal Effect of Cylinder Walls: 

General Ideas, 106, 175 

Heat Interchanges, 209 

Results of Tests, 179-197 
Thermodynamic Availability, 59 

•Cycle, 49 

Efficiency, 53, 232 
Thermodynamics, 33 

General Ideas, 33, 49, 58 

Laws of, 64 
Thermal Properties of Steam, § 13, 

79 
Thiesen's Formula, 617 






INDEX. 



Thomas, Impulse Data, 475 
Throttling Calorimeter, see Steam Calo- 
rimeters 
Throttling, Effect on Steam Consump- 
tion, 186 
Throttling Experiments, 133 
Throttling Governor, 432 

For Turbine, 529 
Throttling or Kinetic Pressure Low- 
ering, § 17, 128 

Continuous, 129 

Energy Transformed in, 130 

Fall of Temperature in, 132 
Tomlinson Condenser, 555 

Water Ejector, 568 
Total Heat, Saturated Steam, 80 

Superheated Steam, 85, 606 
Tube Joint, Surface Condenser, 547 
Turbine Characteristics : 

Directions of Steam Flow, 510 

Double Flow, 514 

Radial Flow, 510 

Tangential Flow, 511 

Types of Steam Action, 32, 510 
Turbine Construction: 

Balance Pistons, 31, 513 

Bearings, 520 

Blading, Impulse, 526, Reaction, 528 

Centrifugal Stress and Balance, 519 

Disc Wheels, 517 

Drum Rotors, 518 

Governors and Valves, 529-534 

Labyrinth Packing, 524 

Nozzles and Distributors, 524 

Pivot Bearing, 522 

Rotors, 516 

Stuffing Boxes, 522 

Vanes or Blades, 526 

Wear on Vanes, 528 
Turbine Design: 

Dimensions of Steam Channel, 503 

Mollier Diagram, Use and Form, 506, 
508 

Multistage Turbine, 504 

Stage-point Locus, 507 

Stages, Proportions of, 508 

*Vane Channels, Proportions of, 509 
Turbine Governing: 

Curtis Governor and Valve, 533 

Cut-off Control, 533 

De Laval Governor and Valve, 529 

Effect of Governor Action, 535 

Parsons Governor and Yalve, 531 

Puff Governing, 530 

Self-acting Valves, 534 

Throttling, 529 
Turbine, Losses of Energy in, 477, 494, 

502 
Turbine Performance, § 48, 477 

By Stages, 495 

Combined Unit, 499 

Estimate of Losses, 502 



629 



of 



Turbine Performance, Influence 
Load Factor, 488 

Influence of Size, 487 

Influence of Steam Condition, 490 

Low-pressure Turbine, 499 

Mollier ^Diagram, Use of, 496 

Pressure Range, Effect of, 491 

Speed and Energy Losses, 494 

Superheating, Effect of, 491 

Table of Tests Results, 478-485 

Vacuum, Effect of, 492 

Various Types, 487 
Turbines : 

Classification of, 32 

Curtis, 27 

De Laval, 24 

Elektra, 510 

Fullager Balancing System, 513 

Geared, 516 

Impulse and Reaction, 23, 28, 422 

Kerr, 511 

Low-pressure and Mixed-flow, 515 

Marine, 515 

Melms-Pfenninger, 512 

Mixed Type, 31 

Multiple-expansion, 25 

Multiple-impulse, 27 

Parsons, 29 

Rateau, 25 

Riedler-Stumpf, 511 

Sulzer, 31 

Variations, Impulse Class, 512 

Variations, Reaction Class, 513 

Westinghouse Double-flow, 514 

Westinghouse-Parsons, 30 

Zoelly, 526 
Turbine Stages, Proportions of, 508 
Turbine Tests, see Turbine Performance 
Turning-force Diagrams, 317 

Ratios, 316 

Relations, 313 
Two Eccentrics, in Corliss Gear, 415 
Types of Condensers, 545 

Of Engine Loading, 275 

Of Shaft Governors, 430 

Of Steam Action in Turbine, 32, 510 

Of Vane Action, 441 

Unit Steam Diagram, 174 

Vacuum Augmenter, Parsons, 564 
Vacuum, Economical, 243 

Effect on Turbine Performance, 492 
Valve Action, Corliss Gear, 410 

Function of Cut-off Valve, 392 

General Action, 17 

Influence and Variation of Lead, 381 

Plain Slide Valve, 365 

Positive and Negative Valve, 393 

Shifting Eccentric Gear, 378 

Symmetrical Admission, 379 

Width of Port Opening, 378 



630 



THE STEAM ENGINE AND TURBINE. 



Valve Chest and Steam Passages, 347 
Valve Diagrams: 

Bilgram Diagram, 371 

Complete Diagram, 365 

Corliss Gear, 410 

For Shaft Governor, 378 

For Stephenson Gear, 387 

Geometrical Relations, 372 

Reuleaux Diagram, 363 . 

Rules for Drawing, 364 

Valve and Piston Diagram, 366 

Zeuner Diagram, 363 
Valve Gear, Outline and Action, 16 
Valve-gear Parts: 

Eccentric and Strap, 401 

Rods and Rockers, 402 
Valve-gear Relations: 

Geometrical Relations, 372 

Lap, Lead, and Advance, 369 

Rocker-arm Effect, 371 

Secondary Disturbances, 372 
Valve Gears and Governors, Chap. 

VIII, 362 
Valve Gears: 

Corliss, 403 

Double- valve, 391 

Duplex Pump, 422 

Joy, 390 

Lift-valve, 417 

Meyer, 391 

Non-harmonic, Shifting Eccentric, 417 

Radial, 388 

Releasing, with Gridiron Valves, 417 

Reversing, 382; for Rolling Mill, 425 

Self-centering, 425 

Shifting-eccentric, 376 

Simplified Form, 362 

Single Pump, Steam Actuated, 423 

Stephenson Link Motion, 382 

Walschaert, 389 

With no Crank Shaft, 421 
Valve Movement: 

Corliss Gear, 409 

Fixed Eccentric, 363 

Link Motion, 385 

Radial Gears, 388 

Relative, of Cut-off Valve, 392 

Rocker-arm Effect, 371 
Valve Resistance, Corliss, 413 

See also Balanced Valves 
Valve Rods, 402 
Valves, Balanced, 397, 399 

B Form, 398^ 

Characteristics of, 396 

Cut-off or Riding, 392 

Dash-relief, 423 

Direct and Indirect, 370 

Flat Balanced, 397 

For Turbines, 530-534 

Lift or Poppet, 418 

Multiple-admission, 399 

Piston, 398 



Valves, Positive and Negative, 393 

Proportions of, 401 

Self-centering, 425 

Steam-actuated, 423 

Various Forms of, 397, 413 
Valve Setting, Corliss, 412 

Plain Slide, 374 
Van den Kerchove Valves, 419 
Vane Action, Types of, 441 
Vane Channels, Proportions of, 509 
Vane of Turbine: 

Action of Jet upon, 439 

Driving Force upon, 440 

Form and Speed, 447 

Work of Steam on, 443 
Vanes, Imoulse upon, Experiments, 475 

For Turbines, 526 

Non-symmetrical, Impulse, 337 

Wear on, 528 
Vaporization, Heat of, 80 

Partial, Heat in, 81 

Volume in Partial, 70 
Variable Steam Distribution, § 39,. 
376 

Double-valve Gear, 394 

Link Motion and Radial Gears, 387, 388 

Shaft Governor, 378 
Variable Compression, Tests with, 206 
Variations of Impulse Turbines, 512 

Of Reaction Turbines, 513 
Various Curves and Operations 

(Steam), § 14, 91 
Various Efficiencies, 234 
Various Engine Tests, 179 
Various Forms of the Turbine, § 50, 

510 
Various Valve-gear Relations, § 38, 

371 
Various Valve Gears, § 44, 417 
Velocity, Absolute, in Vane Channel, 451 
Velocity and Acceleration, in Engine, 303 
Velocity Diagram for Piston, 306 

For Turbine, 439, 450 
Velocity Staging, 27, 450 

Limitations of, 474 
Virtual Eccentric, 392 

Rotating Same, 395 
Volume, Constant: 

Heating Gas, 37 

Heating Steam, 76 
Volume in Partial Vaporization, 70 

Of Air and Vapor Mixture, 549 

Of Superheated Steam, 72 
Volumetric Efficiency of Air Pump, 565 

Walschaert Valve Gear, 389 

Water Ejectors, 566 

Water, External Energy of, 83 

Flow of, 126 

Heat of, 80 

Specific Heat of, 79 

Specific Volume of, 70 






INDEX. 



631 



Wear on Turbine Vanes, 528 
Weight of Fly-wheel, 321 
Westinghouse Double-flow Turbine, 514 
Westinghouse Engine Governor, 430 
Westinghouse-Parsons Turbine, 30 
Wheel, Effective Radius of, 322 

Limit of Speed, 326 

Stress in Rim of, 324 

Weight of, 321 
Wheeler Dry-tube Condenser, 563 
Wheels for Turbines, 517 
Willans Engine Tests, 185 
Willans-Robinson Turbine Blading, 528 
Work and Power, 34 
Work, Disgregation, 41 

External and Internal, 41 

External, of Steam, 82 

On Turbine Vanes, 443 

Per Pound of Steam, 109 

Per Revolution of Engine, 160 



Work, Positive and Negative, 49 
Pressure-volume Measure of, 43 

Working Forces in the Engine, § 32, 
308 
Determining Tangential Force, 315 
Diagrams of Turning Force, 317 
Driving Force at Wrist Pin, 311 
Effective Steam Pressure, 311 
Fly-wheel Data, 318 
Inertia Force of Slide, 308 
Turning-force Relations, 313 

Working and Construction of En- 
gine, Chap. VII, 291 

Working of Auxiliaries, 235 

Working Steam and Clearance Steam, 
146 

Zero, Absolute, 38 

Zeuner Valve Diagram, 363 

Zoelley Turbine, 526 



r 



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Adam, P. Practical Bookbinding. Trans, by T. E. Maw i2mo, *2 50 

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Universal Dictionary of Weights and Measures 8vo, 3 50 

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Anderson, F. A. Boiler Feed Water 8vo, *2 50 

Anderson, Capt. G. L. Handbook for the Use of Electricians 8vo, 3 00 

Anderson, J. W. Prospector's Handbook nmo, 1 50 

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Atkinson, J. J. Friction of Air in Mines. (Science Series No. 14.) . . i6mo, 
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Deerr, N. Sugar and the Sugar Cane 8vo, *3 00 

Deite, C. Manual of Soapmaking. Trans, by S. T. King 4to, *5 00 

De la Coux, H. The Industrial Uses of Water. Trans, by A. Morris . . 8vo, *4 50 

Del Mar,,W. A. Electric Power Conductors 8vo, *2 00 

Denny, G. A. Deep-level Mines of the Rand 4to, *io 00 

Diamond Drilling for Gold *5 00 

De Roos, J. D. C. Linkages. (Science Series No. 47.) i6mo, o 50 

De Varona, A. Sewer Gases. (Science Series No. 55.) i6mo, o 50 

Derr, W. L. Block Signal Operation Oblong i2mo, *i 50 

Desaint, A. Three Hundred Shades and How to Mix Them 8vo, *io 00 

Dibdin, W. J. Public Lighting by Gas and Electricity 8vo, *8 00 

Purification of Sewage and Water 8vo, 6 50 

Dieterich, K. Analysis of Resins, Balsams, and Gum Resins 8vo, *3 00 

Dinger, Lieut. H. C. Care and Operation of Naval Machinery i2mo, *2 00 

Dixon, D. B. Machinist's and Steam Engineer's Practical Calculator. 

i6mo, morocco, 1 25 
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Dodd, G. Dictionary of Manufactures, Mining, Machinery, and the 

Industrial Arts i2mo, 1 50 

Dorr, B. F. The Surveyor's Guide and Pocket Table-book. 

i6mo, morocco, 2 00 

Down, P. B. Handy Copper Wire Table i6mo, *i 00 

Draper, C. H. Elementary Text-book of Light, Heat and Sound. . . i2mo, 1 00 

Heat and the Principles of Thermo-dynamics i2mo, 1 50 

Duckwall, E. W. Canning and Preserving of Food Products 8vo, *$ 00 

Dumesny, P., and Noyer, J. Wood Products, Distillates, and Extracts. 

8vo, *4 50 
Duncan, W. G., and Penman, D. The Electrical Equipment of Collieries. 

8vo, *4 00 



8 D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Duthie, A. L. Decorative Glass Processes. (Westminster Series.)- . 8vo, *2 oo 

Dyson, S. S. Practical Testing of Raw Materials .8vo, *5 oo 

Eccles, R. G., and Duckwall, E. W. Food Preservatives 8vo, i oo 

Paper o 50 

Eddy, H. T. Researches in Graphical Statics 8vo, 1 50 

Maximum Stresses under Concentrated Loads 8vo, 1 50 

Edgcumbe, K. Industrial Electrical Measuring Instruments 8vo, *2 50 

Eissler, M. The Metallurgy of Gold 8vo, 7 50 

The Hydrometallurgy of Copper 8vo, *4 50 

The Metallurgy of Silver 8vo, 4 00 

The Metallurgy of Argentiferous Lead 8vo, 5 00 

Cyanide Process for the Extraction of Gold 8vo, 3 00 

A Handbook on Modern Explosives 8vo, 5 00 

Ekin, T. C. Water Pipe and Sewage Discharge Diagrams folio, *3 00 

Eliot, C. W., and Storer, F- H. Compendious Manual of Qualitative 

Chemical Analysis i2mo, *i 25 

Elliot, Major G. H. European Light-house Systems 8vo, 5 00 

Ennis, Wm. D. Linseed Oil and Other Seed Oils 8vo, *4 00 

Applied Thermodynamics 8vo *4 50 

Erfurt, J. Dyeing of Paper Pulp. Trans, by J. Hubner 8vo, *7 50 

Erskine-Murray, J. A Handbook of Wireless Telegraphy 8vo, *3 50 

Evans, C. A. Macadamized Roads {In Press.) 

Ewing, A. J. Magnetic Induction in Iron 8vo, *4 00 

Fairie, J. Notes on Lead Ores i2mo, *i 00 

Notes on Pottery Clays i2mo, *i 50 

Fairley, W., and Andre, Geo. J. Ventilation of Coal Mines. (Science 

Series No. 58.) i6mo, o 50 

Fairweather, W. C. Foreign and Colonial Patent Laws 8vo, *3 00 

Fanning, J. T. Hydraulic and Water-supply Engineering 8vo, *5 00 

Fauth, P. The Moon in Modern Astronomy. Trans, by J. McCabe. 

8vo, *2 00 

Fay, I. W. The Coal-tar Colors 8vo {In Press.) 

Fernbach, R. L. Glue and Gelatine 8vo, *3 00 

Fischer, E. The Preparation of Organic Compounds. Trans, by R. V. 

Stanford i2mo, *i 25 

Fish, J. C. L. Lettering of Working Drawings Oblong 8vo, 1 00 

Fisher, H. K. C, and Darby, W. C. Submarine Cable Testing 8vo, *3 50 

Fiske, Lieut. B. A. Electricity in Theory and Practice. 8vo, 2 50 

Fleischmann, W. The Book of the Dairy. Trans, by C. M. Aikman. 8vo, 4 00 
Fleming, J. A. The Alternate-current Transformer. Two Volumes. 8vo. 

Vol. I. The Induction of Electric Currents *5 00 

Vol. n. The Utilization of Induced Currents *5 00 

Centenary of the Electrical Current 8vo, *o 50 

Electric Lamps and Electric Lighting 8vo, *3 00 

Electrical Laboratory Notes and Forms 4to, *5 00 

A Handbook for the Electrical Laboratory and Testing Room. Two 

Volumes 8vo, each, *5 00 

Fluery, H. The Calculus Without Limits or Infinitesimals. Trans, by 
C. 0. Mailloux {In Press.) 



I 


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Flynn, P. J, Flow of Water. (Science Series No. 84.) i6mo, o 50 

Hydraulic Tables. (Science Series No. 66.) i6mo, o 50 

Foley, N. British and American Customary and Metric Measures, .folio, *3 00 
Foster, H. A. Electrical Engineers' Pocket-book. (Sixth Edition.) 

i2mo, leather, 5 00 
Foster, Gen. J. G. Submarine Blasting in Boston (Mass.) Harbor.. . 4to, 3 50 

Fowle, F. F. Overhead Transmission Line Crossings i2mo, *i 50 

The Solution of Alternating Current Problems 8vo (In Press.) 

Fox, W. G. Transition Curves. (Science Series No. no.).. i6mo, o 50 

Fox, W., and Thomas, C. W. Practical Course in Mechanical Draw- 
ing i2mo, 

Foye, J. C. Chemical Problems. (Science Series No. 69.)... i6mo, 

Handbook of Mineralogy. (Science Series No. 86.) i6mo, 

Francis, J. B. Lowell Hydraulic Experiments 4to, 

Frye, A. I. Civil Engineers' Pocket-book (In Press.) 

Fuller, G. W. Investigations into the Purification of the Ohio River. 4to, *io 00 
Furnell, J. Paints, Colors, Oils, and Varnishes 8vo, *i 00 

Gant, L. W. Elements of Electric Traction 8vo, 

Garcke, E., and Fells, J. M. Factory Accounts 8vo, 

Garforth, W. E. Rules for Recovering Coal Mines after Explosions and 

Fires i2mo, leather, 

Gaudard, J. Foundations. (Science Series No. 34.) i6mo, 

Gear, H. B., and Williams, P. F. Electric Central Station Distributing 

Systems 8vo (In Preparation.) 

Geerligs, H. C. P. Cane Sugar and Its Manufacture 8vo, 

Geikie, J. Structural and Field Geology ! 8vo, 

Gerber, N. Analysis of Milk, Condensed Milk, and Infants' Milk-Food. 8vo, 
Gerhard, W. P. Sanitation, Watersupply and Sewage Disposal of Country 

Houses i2mo, 

Gas Lighting. (Science Series No. in.) i6mo, 

Household Wastes. (Science Series No. 97.) i6mo, 

: House Drainage. (Science Series No. 63.) i6mo, 

Sanitary Drainage of Buildings. (Science Series No. 93.) .... i6mo, 

Gerhardi, C. W. H. Electricity Meters 8vo, 

Geschwind, L. Manufacture of Alum and Sulphates. Trans, by C. 

Salter 8vo, 

Gibbs, W. E. Lighting by Acetylene i2mo, 

Physics of Solids and Fluids. (Carnegie Technical School's Text- 
books.) *i 

Gibson, A. H. Hydraulics and Its Application 8vo, 

Water Hammer in Hydraulic Pipe Lines i2mo, 

Gilbreth, F. B. Motion Study i2mo, 

Gillmore, Gen. Q. A. Limes, Hydraulic Cements and Mortars 8vo, 

Roads, Streets, and Pavements i2mo, 

Golding, H. A. The Theta-Phi Diagram "mo, 

Goldschmidt, R. Alternating Current Commutator Motor 8vo, 

Goodchild, W. Precious Stones. (Westminster Series.) 8vo, 

Goodeve, T. M. Textbook on the Steam-engine i2mo, 

Gore, G. Electrolytic Separation of Metals 8vo, 

Gould, E. S. Arithmetic of the Steam-engine i2mo, 



*2 


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10 D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Gould, E. S. Calculus. (Science Series No. 112.) i6mo, o 50 

High Masonry Dams. (Science Series No. 22.) = i6mo, o 50 

Practical Hydrostatics and Hydrostatic Formulas. (Science Series 

No. 117.) i6mo, o 50 

Grant, J. Brewing and Distilling. (Westminster Series.) 8vo {In Press.) 

Gray, J. Electrical Influence Machines i2mo, 2 00 

Greenwood, E. Classified Guide to Technical and Commercial Books. 8vo, *3 00 

Gregorius, R. Mineral Waxes. Trans, by C. Salter. nmo, *3 00 

Griffiths, A. B. A Treatise on Manures i2mo, 3 00 

Dental Metallurgy, 8vo, *3 50 

Gross, E. Hops 8vo, *4 50 

Grossman, J. Ammonia and Its Compounds i2ino, *i 25 

Groth, L. A. Welding and Cutting Metals by Gases or Electricity. . . .8vo, *3 00 

Grover, F. Modern Gas and Oil Engines 8vo, *2 00 

Gruner, A. Power-loom Weaving 8vo, *3 00 

Giildner, Hugo. Internal Combustion Engines. Trans, by H. Diederichs. 

4to, *io 00 

Gunther, C. 0. Integration nmo, *i 25 

Gurden, R. L. Traverse Tables folio, half morocco, 7 50 

Guy, A. E. Experiments on the Flexure of Beams 8vo, *i 25 

Haeder, H. Handbook on the Steam-engine. Trans, by H. H. P. 

Powles i2mo, 

Hainbach, R. Pottery Decoration. Trans, by C. Slater nmo, 

Hale, W. J. Calculations of General Chemistry i2mo, 

Hall, C. H. Chemistry of Paints and Paint Vehicles nmo, 

Hall, R. H. Governors and Governing Mechanism. nmo, 

Hall, W. S. Elements of the Differential and Integral Calculus 8vo, 

Descriptive Geometry 8vo volume and a 4to atlas, 

Haller, G. F., and Cunningham, E. T. The Tesla Coil.. nmo, 

Halsey, F. A. Slide Valve Gears nmo, 

The Use of the Slide Rule. (Science Series No. 114.) i6mo, 

Worm and Spiral Gearing. (Science Series No. 116.). i6mo, 

Hamilton, W. G. Useful Information for Railway Men i6mo, 

Hammer, W. J. Radium and Other Radio-active Substances 8vo, 

Hancock, H. Textbook of Mechanics and Hydrostatics 8vo, 

Hardy, E. Elementary Principles of Graphic Statics nmo, 

Harper, W. B. Utilization of Wood Waste by Distillation. 4to, 

Harrison, W. B. The Mechanics' Tool-book nmo, 

Hart, J. W. External Plumbing Work 8vo, 

Hints to Plumbers on Joint Wiping 8vo, 

Principles of Hot Water Supply 8vo, 

Sanitary Plumbing and Drainage 8vo, 

Haskins, C. H. The Galvanometer and Its Uses i6mo, 

Hatt, J. A. H. The Colorist square nmo, 

Hausbrand, E. Drying by Means of Air and Steam. Trans, by A. C. 

Wright nmo, *2 00 

Evaporating, Condensing and Cooling Apparatus. Trans, by A. C. 

Wright 8vo, *5 00 

Hausner, A. Manufacture of Preserved Foods and Sweetmeats. Trans. 

by A. Morris and H. Robson 8vo, *3 00 



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D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 11 

Hawke, W. H. Premier Cipher Telegraphic Code 4to, 

100,000 Words Supplement to the Premier Code 4to, 

Hawkesworth, J. Graphical Handbook for Reinforced Concrete Design. 

4to, 

Hay, A. Alternating Currents 8vo, 

Principles of Alternate-current Working i2mo, 

Electrical Distributing Networks and Distributing Lines 8vo, 

Continuous Current Engineering 8vo, 

Heap, Major D. P. Electrical Appliances 8vo, 

Heaviside, 0. Electromagnetic Theory. Two Volumes 8vo, each, 

Heck, R. C. H. Steam-Engine and Other Steam Motors. Two Volumes. 

Vol. I. Thermodynamics and the Mechanics 8vo, 

Vol. II. Form, Construction, and Working 8vo, 

Abridged edition of above volumes (Elementary) 8vo (In Preparation.) 

Notes on Elementary Kinematics 8vo, boards, 

Graphics of Machine Forces 8vo, boards, 

Hedges, K. Modern Lightning Conductors 8vo, 

Heermann, P. Dyers' Materials. Trans, by A. C. Wright nmo, 

Hellot, Macquer and D'Apligny. Art of Dyeing Wool, Silk and Cotton. 

8vo, 

Henrici, 0. Skeleton Structures 8vo, 

Hermann, F. Painting on Glass and Porcelain . 8vo, 

Herrmann, G. The Graphical Statics of Mechanism. Trans, by A. P. 

Smith i2mo, 

Herzfeld, J. Testing of Yarns and Textile Fabrics 8vo, 

Hildebrandt, A. Airships, Past and Present 8vo, 

Hildenbrand, B. W. Cable-Making. (Science Series No. 32.) i6mo, 

Hill, J, W. The Purification of Public Water Supplies. New Edition. ( In Pirns.) 

Interpretation of Water Analysis (In Press.) 

Hiroi, I. Plate Girder Construction. (Science Series No. 95.) i6mo, o 50 

Statically-Indeterminate Stresses nmo, *2 00 

Hirshfeld, C. F. Engineering Thermodynamics. (Science Series No. 45.) 

i6mo, o 50 

Hobart, H. M. Heavy Electrical Engineering 8vo, *4 50 

Electricity 8vo, *2 00 

Electric Trains 8vo, *2 50 

Hobbs, W. R. P. The Arithmetic of Electrical Measurements nmo, o 50 

Hoff, J. N. Paint and Varnish Facts and Formulas i2mo, *i 50 

Hoff, Com. W. B. The Avoidance of Collisions at Sea. . . i6mo, morocco, o 75 

Hole, W. The Distribution of Gas 8vo, +7 50 

Holley, A. L. Railway Practice folio, 12 00 

Holmes, A. B. The Electric Light Popularly Explained .... nmo, paper, o 50 

Hopkins, N. M. Experimental Electrochemistry 8vo, *3 00 

Model Engines and Small Boats nmo, 1 25 

Hopkinson, J. Shoolbred, J ; N., and Day, R. E. Dynamic Electricity. 

(Science Series No. 71.) i6mo, o 50 

Horner, J. Engineers' Turning 8vo, *3 50 

Metal Turning i2mo, 1 50 

Toothed Gearing i2mo, 2 25 

Houghton, C. E. The Elements of Mechanics of Materials nmo, *2 00 

Houllevique, L. The Evolution of the Sciences 8vo, *2 00 



*5 


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12 D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Howe, G. Mathematics for the Practical Man nmo, *i 25 

Howorth, J. Repairing and Riveting Glass, China and Earthenware. 

8vo, paper, 

Hubbard, E. The Utilization of Wood- waste 8vo, 

Humber, W. Calculation of Strains in Girders nmo, 

Humphreys, A. C, The Business Features of Engineering Practice. . 8vo, 

Hurst, G. H. Handbook of the Theory of Color 8vo, 

Dictionary of Chemicals and Raw Products 8vo, 

Lubricating Oils, Fats and Greases 8vo, 

Soaps 8 vo, 

Textile Soaps and Oils 8vo, 

Hurst, H. E., and Lattey, R. T. Text-book of Physics 8vo, 

Hutchinson R. W., Jr. Long Distance Electric Power Transmission . i2mo, 
Hutchinson, R. W., Jr., and Ihlseng, M. C. Electricity in Mining. . nmo, 

(In Press) 
Hutchinson, W. B. Patents and How to Make Money Out of Them. 

i2mo, 1 25 

Hutton, W. S. Steam-boiler Construction 8vo, 6 00 

Practical Engineer's Handbook 8vo, 7 00 

The Works' Manager's Handbook 8vo, 6 00 

Hyde, E. W. Skew Arches. (Science Series No. 15.) i6mo, o 50 

Induction Coils. (Science Series No. 53.) i6mo, o 50 

Ingle, H. Manual of Agricultural Chemistry 8vo, 

Innes, C. H. Problems in Machine Design i2mo, 

Air Compressors and Blowing Engines nmo, 

Centrifugal Pumps nmo, 

The Fan nmo, 

Isherwood, B. F. Engineering Precedents for Steam Machinery 8vo, 

Ivatts, E. B. Railway Management at Stations 8vo, 

Jacob, A., and Gould, E. S. On the Designing and Construction of 

Storage Reservoirs. (Science Series No. 6.) i6mo, 

Jamieson, A. Text Book on Steam and Steam Engines 8vo, 

Elementary Manual on Steam and the Steam Engine nmo, 

Jannettaz, E. Guide to the Determination of Rocks. Trans, by G. W. 

Plympton ' nmo, 

Jehl, F. Manufacture of Carbons 8vo, 

Jennings, A. S. Commercial Paints and Painting. (Westminster Series.) 

8vo (In Press.) 

Jennison, F. H. The Manufacture of Lake Pigments 8vo, 

Jepson, G. Cams and the Principles of their Construction 8vo, 

Mechanical Drawing 8vo (In Preparation.) 

Jockin, W. Arithmetic of the Gold and Silversmith nmo, 

Johnson, G. L. Photographic Optics and Color Photography 8vo, 

Johnson, W. H. The Cultivation and Preparation of Para Rubber. . .8vo, 

Johnson, W. McA. The Metallurgy of Nickel (In Preparation.) 

Johnston, J. F. W., and Cameron, C. Elements of Agricultural Chemistry 

and Geology nmo, 

Joly, J. Raidoactivity and Geology nmo, 

Jones, H. C. Electrical Nature of Matter and Radioactivity nmo, 



"-3 


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00 


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D. VAX NOSTRAND COMPANY'S SHORT TITLE CATALOG 13 

Jones, M. W. Testing Raw Materials Used in Paint i2mo, *2 oo 

Jones, L., and Scard, F. I. Manufacture of Cane Sugar 8vo, *5 oo 

Joy, G. A., and Thiess, J. B. Toll Telephone Practice {In Press.) 

Joynson, F. H. Designing and Construction of Machine Gearing. . . 8vo, 2 00 

Jiiptner, H. F. V. Siderology: The Science of Iron 8vo, *5 00 

Kansas City Bridge 4to, 6 00 

Kapp, G. Alternate Current Machinery. (Science Series No. 96.) . i6mo, o 50 

Dynamos, Motors, Alternators and Rotary Converters. Trans, by 

H. H. Simmons 8vo, 4 00 

Electric Transmission of Energy i2mo, 3 50 

Keim, A. W. Prevention of Dampness in Buildings 8vo, *2 00 

Keller, S. S. Mathematics for Engineering Students. 121110, half leather. 

Algebra and Trigonometry, with a Chapter on Vectors *i 75 

Special Algebra Edition *i 00 

Plane and Solid Geometry *i 25 

Analytical Geometry and Calculus *2 00 

Kelsey, W. R. Continuous-current Dynamos and Motors 8vo, *2 50 

Kemble, W. T., and Underhill, C. R. The Periodic Law and the Hydrogen 

Spectrum 8vo, paper, *o 50 

Kemp, J. F. Handbook of Rocks 8vo, *i 50 

Kendall, E. Twelve Figure Cipher Code 4to, *i5 00 

Kennedy, A. B. W., and Thurston, R. H. Kinematics of Machinery. 

(Science Series No. 54.) i6mo, o 50 

Kennedy, A. B. W., Unwin, W. C, and Idell, F. E. Compressed Air. 

(Science Series No. 106.) i6mo, o 50 

Kennedy, R. Modern Engines and Power Generators. Six Volumes. 4to, 15 00 

Single Volumes each, 3 00 

Electrical Installations. Five Volumes 4to, 15 00 

Single Volumes each, 3 50 

Flying Machines; Practice and Design 121110, *2 00 

Kennelly, A. E. Electro-dynamic Machinery 8vo, 1 50 

Kent, W. Strength of Materials. (Science Series No. 41.) i6mo, o 50 

Kershaw, J. B. C. Fuel, Water and Gas Analysis 8vo, *2 50 

Electrometallurgy. (Westminster Series.) 8vo, *2 00 

Kershaw, J. B. C. The Electric Furnace in Iron and Steel Production. 

i2mo, *i 50 

Kingdon, J. A. Applied Magnetism 8vo, *3 00 

Kinzbrunner, C. Alternate Current Windings 8vo, *i 50 

Continuous Current Armatures 8vo, *i 50 

Testing of Alternating Current Machines 8vo, *2 00 

Kirkaldy, W. G. David Kirkaldy's System of Mechanical Testing 4to, 10 00 

Kirkbride, J. Engraving for Illustration 8vo, *i 50 

Kirkwood, J. P. Filtration of River Waters 4*o, 7 5° 

Klein, J. F. Design of a High-speed Steam-engine 8vo, *5 00 

Physical Significance of Entropy 8vo, *i 50 

Kleinhans, F. B. Boiler Construction 8vo, 3 00 

Knight, Lieut.-Com. A. M. Modern Seamanship 8vo, *6 00 

Half morocco *7 5° 

Knox, W. F. Logarithm Tables (In Preparation.) 

Knott, C. G., and Mackay, J. S. Practical Mathematics 8vo, 2 00 



14 D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Koester, F. Steam-Electric Power Plants 4to, *5 oo 

Hydroelectric Developments and Engineering . 4to, *5 oo 

Koller, T. The Utilization of Waste Products 8vo, *3 50 

Cosmetics 8vo, *2 50 

Krauch, C. Testing of Chemical Reagents. Trans, by J. A. Williamson 

and L. W. Dupre 8vo, *3 00 

Lambert, T. Lead and its Compounds 8vo, *3 50 

Bone Products and Manures 8vo, *3 00 

Lamborn, L. L. Cottonseed Products 8vo, *3 00 

Modern Soaps, Candles, and Glycerin 8vo, *7 50 

Lamprecht, R. Recovery Work After Pit Fires. Trans, by C. Salter . . 8vo, *4 00 
Lanchester, F. W. Aerial Flight. Two Volumes. 8vo. 

Vol. I. Aerodynamics *6 00 

Vol. II. Aerodonetics *6 00 

Larner, E. T. Principles of Alternating Currents i2mo, *i 25 

Larrabee, C. S. Cipher and Secret Letter and Telegraphic Code. . . . i6mo, o 60 

La Rue, B. F. Swing Bridges. (Science Series No. 107.) i6mo, o 50 

Lassar-Cohn, Dr. Modern Scientific Chemistry. Trans, by M. M. Patti- 

son Muir i2mo, *2 00 

Latimer, L. H., Field, C. J., and Howell, J. W. Incandescent Electric 

Lighting. (Science Series No. 57.) i6mo, o 50 

Latta, M. N. Handbook of American Gas-Engineering Practice 8vo, *4 50 

American Producer Gas Practice 4to, *6 00 

Leask, A. R. Breakdowns at Sea nmo, 2 00 

Triple and Quadruple Expansion Engines nmo, 2 00 

Refrigerating Machinery nmo, 2 00 

Lecky, S. T. S. " Wrinkles " in Practical Navigation 8vo, *8 00 

Le Doux, M. Ice-Making Machines. (Science Series No. 46.) .... i6mo, o 50 

Leeds, C. C. Mechanical Drawing for Trade Schools oblong 4to, 

High School Edition -. *i 25 

Machinery Trades Edition *2 00 

Lefe*vre, L. Architectural Pottery. Trans, by H. K. Bird and W. M. 

Binns 4to, *7 50 

Lehner, S. Ink Manufacture. Trans, by A. Morris and H. Robson . . 8vo, *2 50 

Lemstrom, S. Electricity in Agriculture and Horticulture 8vo, *i 50 

Le Van, W. B. Steam-Engine Indicator. (Science Series No. 78.) . i6mo, o 50 

Lewes, V. B. Liquid and Gaseous Fuels. (Westminster Series.). .. .8vo, *2 00 

Lieber, B. F. Lieber's Standard Telegraphic Code 8vo, *io 00 

Code. German Edition ,. ._ ■. . .8vo, *io 00 

Spanish Edition 8vo, *io 00 

French Edition 8vo, *io 00 

Terminal Index 8vo, *2 50 

Lieber's Appendix folio, *i5 00 

Handy Tables 4to, *2 50 

Bankers and Stockbrokers' Code and Merchants and Shippers' Blank 

Tables 8vo, *i5 00 

100,000,000 Combination Code 8vo, *i5 00 

Engineering Code 8vo, *io 00 

Livermore, V. P., and Williams, J. How to Become a Competent Motor- 
man i2mo, *i 00 



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D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 15 

Livingstone, R. Design and Construction of Commutators 8vo, 

Lobben, P. Machinists' and Draftsmen's Handbook 8vo, 

Locke, A. G. and C. G. Manufacture of Sulphuric Acid 8vo, 

Lockwood, T. D. Electricity, Magnetism, and Electro-telegraph. 

8vo, 

Electrical Measurement and the Galvanometer i2mo, 

Lodge, 0. J. Elementary Mechanics i2mo, 

Signalling Across Space without Wires 8vo, 

Lord, R. T. Decorative and Fancy Fabrics 8vo, 

Loring, A. E. A Handbook of the Electromagnetic Telegraph i6mo, 

Handbook. (Science Series No. 39.) i6mo, 

Lowenstein, L. C, and Crissey, C. P. Centrifugal Pumps. . . . (In Press.) 

Lucke, C. E. Gas Engine Design 8vo, *3 00 

Power Plants: their Design, Efficiency, and Power Costs. 2 vols. 

(In Preparation.) 

Power Plant Papers. Form I. The Steam Power Plant paper, *i 50 

Lunge, G. Coal-tar and Ammonia. Two Volumes 8vo, *i5 00 

Manufacture of Sulphuric Acid and Alkali. Three Volumes .... 8vo, 

Vol. I. Sulphuric Acid. In two parts *i5 00 

Vol. II. Salt Cake, Hydrochloric Acid and Leblanc Soda. In two 

parts *i5 00 

Vol. III. Ammonia Soda *i5 00 

Technical Chemists' Handbook nmo, leather, *3 50 

Technical Methods of Chemical Analysis. Trans, by C. A. Keane. 

in collaboration with the corps of specialists. 

Vol. I. In two parts 8vo, *i5 00 

Vols. II and III (In Preparation.) 

Lupton, A., Parr, G. D. A., and Perkin, H. Electricity as Applied to 

Mining 8vo, 

Luquer, L. M. Minerals in Rock Sections 8vo, 

Macewen, H. A. Food Inspection 8vo, 

Mackenzie, N. F. Notes on Irrigation Works 8vo, 

Mackie, J. How to Make a Woolen Mill Pay 8vo, 

Mackrow, C. Naval Architect's and Shipbuilder's Pocket-book. 

i6mo, leather, 
Maguire, Capt. E. The Attack and Defense of Coast Fortifications. . . 8vo, 

Maguire, Wm. R. Domestic Sanitary Drainage and Plumbing 8vo, 

Mallet, A. Compound Engines. Trans, by R. R. Buel. (Science Series 

No. 10.) i6mo, 

Mansfield, A. N. Electro-magnets. (Science Series No. 64.) i6mo, 

Marks, E. C. R. Construction of Cranes and Lifting Machinery. . . . i2mo, 

Construction and Working of Pumps i2mo, 

Manufacture of Iron and Steel Tubes i2mo, 

Mechanical Engineering Materials i2mo, 

Marks, G. C. Hydraulic Power Engineering 8vo, 

Inventions, Patents and Designs i2mo, 

Markham, E. R. The American Steel Worker i2mo, 

Marlow, T. G. Drying Machinery and Practice 8vo, 

Marsh, C. F. Concise Treatise on Reinforced Concrete 8vo, 

Marsh, C. F., and Dunn, W. Reinforced Concrete 4 to > 



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16 D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Marsh, C. F., and Dunn, W. Manual of Reinforced Concrete and Con- 
crete Block Construction i6mo, morocco, *2 50 

Massie, W. W., and Under hill, C. R. Wireless Telegraphy and Telephony. 

i2mo, *i 00 
Matheson, D. Australian Saw-Miller's Log and Timber Ready Reckoner. 

i2mo, leather, 1 50 

Mathot, R. E. Internal Combustion Engines 8vo, *6 00 

Maurice, W. Electric Blasting Apparatus and Explosives 8vo, 

Shot Firer's Guide 8vo, 

Maxwell, J. C. Matter and Motion. (Science Series No. 36.) i6mo, 

Maxwell, W. H., and Brown, J. T. Encyclopedia of Municipal and Sani- 
tary Engineering 4to, 

Mayer, A. M. Lecture Notes on Physics 8vo, 

McCullough, R. S. Mechanical Theory of Heat 8vo, 

Mcintosh, J. G. Technology of Sugar 8vo, 

— — Industrial Alcohol 8vo, 

Manufacture of Varnishes and Kindred Industries. Three Volumes. 

8vo. 

Vol. I. Oil Crushing, Refining and Boiling *3 50 

Vol. II. Varnish Materials and Oil Varnish Making *4 00 

Vol. Ill (In Preparation.) 

McKnight, J. D., and Brown, A. W. Marine Multitubular Boilers *i 50 

McMaster, J. B. Bridge and Tunnel Centres. (Science Series No. 20.) 

i6mo, 

McMechen, F. L. Tests for Ores, Minerals and Metals i2mo, 

McNeill, B. McNeill's Code 8vo, 

McPherson, J. A. Water- works Distribution 8vo, 

Melick, C. W. Dairy Laboratory Guide 12010, 

Merck, E. Chemical Reagents; Their Purity and Tests 8vo, 

Merritt, Wm. H. Field Testing for Gold and Silver i6mo, leather, 

Meyer, J. G. A., and Pecker, C. G. Mechanical Drawing and Machine 

Design 4to 5 

Michell, S. Mine Drainage 8vo, 

Mierzinski, S. Waterproofing of Fabrics. Trans, by A. Morris and H. 

Robsoh 8vo, 

Miller, E. H. Quantitative Analysis for Mining Engineers . .8vo, 

Miller, G. A. Determinants. (Science Series No. 105.) i6mo, 

Milroy, M. E. W. Home Lace-making i2mo, 

Minifie, W. Mechanical Drawing 8vo, 

Mitchell, C. A., and Prideaux, R. M. Fibres Used in Textile and Allied 

Industries 8vo, 

Modern Meteorology i2mo, 

Monckton, C. C. F. Radiotelegraphy. (Westminster Series.) 8vo, 

Monteverde, R. D. Vest Pocket Glossary of English-Spanish, Spanish- 
English Technical Terms 643110, leather, *i 00 

Moore, E. C. S. New Tables for the Complete Solution of Ganguillet and 

Kutter's Formula 8vo, *5 00 

Moreing, C. A., and Neal, T. New General and Mining Telegraph Code, 8vo, *5 00 

Morgan, A. P. Wireless Telegraph Apparatus for Amateurs 121110, *i 50 

Moses, A. J. The Characters of Crystals 8vo, *2 00 

Moses, A. J., and Parsons, C. L. Elements of Mineralogy 8vo, *2 50 






50 


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D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 17 

Moss, S. A. Elements of Gas Engine Design. (Science Series No.i2i.)i6mo, 

The Lay-out of Corliss Valve Gears. (Science Series No. 119.) i6mo, 

Mullin, J. P. Modern Moulding and Pattern-making i2mo, 

Munby, A. E. Chemistry and Physics of Building Materials. (Westmin- 
ster Series.) 8 V0 

Murphy, J. G. Practical Mining i6mo 

Murray, J. A. Soils and Manures. (Westminster Series.) 8vo, 

Naquet, A. Legal Chemistry i2mo, 

Nasmith, J. The Student's Cotton Spinning 8vo, 

Neilson, R. M. Aeroplane Patents 8vo, 

Nerz, F. Searchlights. Trans, by C. Rodgers 8vo, 

Neuberger, H., and Noalhat, H. Technology of Petroleum. Trans, by J. 

G. Mcintosh 8vo, 

Newall, J. W. Drawing, Sizing and Cutting Bevel-gears 8vo, 

Newlands, J. Carpenters and Joiners' Assistant. folio, half morocco, 

Nicol, G. Ship Construction and Calculations 8vo, 

Nipher, F. E. Theory of Magnetic Measurements i2mo, 

Nisbet, H. Grammar of Textile Design , 8vo, 

Nolan, H. The Telescope. (Science Series No. 51.) i6mo, 

Noll, A. How to Wire Buildings *..... nmo, 

Nugent, E. Treatise on Optics i2mo, 

O'Connor, H. The Gas Engineer's Pocketbook nmo, leather, 

Petrol Air Gas i2mo, 

Ohm, G. S., and Lockwood, T. D. Galvanic Circuit. Translated by 

William Francis. (Science Series No. 102.) i6mo, o 50 

Olsson, A. Motor Control, in Turret Turning and Gun Elevating. (U. S. 

Navy Electrical Series, No. 1.) i2mo, paper, *o 50 

Olsen, J. C. Text-book of Quantitative Chemical Analysis 8vo, +4 00 

Oudin, M. A. Standard Polyphase Apparatus and Systems 8vo, *3 00 

Palaz, A. Industrial Photometry. Trans, by G. W. Patterson, Jr. . . 8vo, *4 00 

Pamely, C. Colliery Manager's Handbook 8vo, *io 00 

Parr, G. D. A. Electrical Engineering Measuring Instruments 8vo, *3 50 

Parry, E. J. Chemistry of Essential Oils and Artificial Perfumes . . 8vo, *5 00 

Parry, E. J., and Coste, J. H. Chemistry of Pigments 8vo, *4 50 

Parry, L. A. Risk and Dangers of Various Occupations 8vo, *3 00 

Parshall, H. F., and Hobart, H. M. Armature Windings 4to, *7 50 

Electric Railway Engineering 4to, *io 00 

Parshall, H. F., and Parry, E. Electrical Equipment of Tramways. (/// Press.) 

Parsons, S. J. Malleable Cast Iron 8vo, *2 50 

Passmore, A. C. Technical Terms Used in Architecture 8vo, *3 50 

Patterson, D. The Color Printing of Carpet Yarns 8vo, *3 50 

Color Matching on Textiles 8vo, *3 00 

The Science of Color Mixing 8vo, *3 00 

Patton, H. B. Lecture Notes on Crystallography 8vo, *i 25 

Paulding, C. P. Condensation of Steam in Covered and Bare Pipes. 8vo, *2 00 

Transmission of Heat through Cold-storage Insulation 12 mo, *i 00 

Peirce, B. System of Analytic Mechanics 4to, 10 00 

Pendred, V. The Railway Locomotive. (Westminster Series.) 8vo, *2 00 

Perkin, F. M. Practical Methods of Inorganic Chemistry nmo, *i 00 



18 D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Perrigo, 0. E. Change Gear Devices 8vo, i oo 

Perrine, F. A. C. Conductors for Electrical Distribution . 8vo, *3 50 

Petit, G. White Lead and Zinc White Paints 8vo, *i 50 

Petit, R. How to Build an Aeroplane. Trans, by T. O'B. Hubbard, and 

J. H. Ledeboer 8vo, *i 50 

Pettit, Lieut. J. S. Graphic Processes. (Science Series No. 76.) . . . i6mo, o 50 

Perry, J. Applied Mechanics 8vo, *2 50 

Philbrick, P. H. Beams and Girders. (Science Series No. 88.) . . . i6mo, 

Phillips, J. Engineering Chemistry 8vo, *4 50 

Gold Assaying 8vo, *2 50 

Dangerous Goods 8vo, 3 50 

Phin, J. Seven Follies of Science. nmo, *i 25 

■ Household Pests, and How to Get Rid of Them 8vo (In Preparation.) 

Pickworth, C. N. The Indicator Handbook. Two Volumes. . i2mo, each, 1 50 

Logarithms for Beginners nmo, boards, o 50 

The Slide Rule. . i2mo, 1 00 

Plane Table, The 8vo, 2 00 

Plattner's Manual of Blow-pipe Analysis. Eighth Edition, revised. Trans. 

by H. B. Cornwall 8vo, *4 00 

Plympton, G. W. The Aneroid Barometer. (Science Series No. 35.) i6mo, o 50 

How to become an Engineer. (Science Series No. 100.) i6mo, o 50 

Van Nostrand's Table Book. (Science Series No. 104.) i6mo, o 50 

Pochet, M. L. Steam Injectors. Translated from the French. (Science 

Series No. 29.) i6mo, o 50 

Pocket Logarithms to Four Places. (Science Series No. 65.) i6mo, o 50 

leather, 1 00 

Pope, F. L. Modern Practice of the Electric Telegraph 8vo, 1 50 

Popplewell, W. C. Elementary Treatise on Heat and Heat Engines. . i2mo, *3 00 

Prevention of Smoke 8vo, *3 50 

Strength of Materials 8vo, *i 75 

Potter, T. Concrete 8vo, *3 00 

Practical Compounding of Oils, Tallow and Grease 8vo, *3 50 

Practical Iron Founding nmo, 1 50 

Pray, T., Jr. Twenty Years with the Indicator 8vo, 2 50 

Steam Tables and Engine Constant 8vo, 2 00 

Calorimeter Tables . 8vo, 1 00 

Preece, W. H. Electric Lamps (In Press.) 

Prelini, C. Earth and Rock Excavation 8vo, *3 00 

Graphical Determination of Earth Slopes 8vo, *2 00 

Tunneling 8 vo, 3 00 

Dredging. A Practical Treatise (In Press.) 

Prescott, A. B. Organic Analysis 8vo, 5 00 

Prescott, A. B., and Johnson, 0. C. Qualitative Chemical Analysis. . .8vo, *3 50 
Prescott, A. B., and Sullivan, E. C. First Book in' Qualitative Chemistry. 

i2mo, *i 50 

Pritchard, O. G. The Manufacture of Electric-light Carbons . . 8vo, paper, *o 60 
Prost, E. Chemical Analysis of Fuels, Ores, Metals. Trans, by J. C. 

Smith 8vo, *4 50 

Pullen, W. W. F. Application of Graphic Methods to the Design of 

Structures nmo, *2 50 

Injectors: Theory, Construction and Working i2mo, *i 50 



D. VAN NOSTRAXD COMPANY'S SHORT TITLE CATALOG 19 

Pulsifer, W. H. Notes for a History of Lead 8vo, 4 00 

Purchase, W. R. Masonry i2mo, *3 00 

Putsch, A. Gas and Coal-dust Firing 8vo, *3 00 

Pynchon, T. R. Introduction to Chemical Physics 8vo, 3 00 

Rafter G. W. Mechanics of Ventilation. (Science Series No. 33.) . i6mo, 

Potable Water. (Science Series No. 103.) i6mo, 

Treatment of Septic Sewage. (Science Series No. 118.) i6mo, 

Rafter, G. W., and Baker, M. N. Sewage Disposal in the United States . 4 to, 

Raikes, H. P. Sewage Disposal Works 8vo, 

Railway Shop Up-to-Date 4to, 

Ramp, H. M. Foundry Practice (In Press.) 

Randall, P. M. Quartz Operator's Handbook.. nmo, 

Randau, P. Enamels and Enamelling 8vo, 

Rankine, W. J. M. Applied Mechanics 8vo, 

Civil Engineering 8vo, 

Machinery and Millwork 8vo, 

Rankine, W. J. M. The Steam-engine and Other Prime Movers 8vo, 

Useful Rules and Tables 8vo, 

Rankine, W. J. M., and Bamber, E. F. A Mechanical Text-book. . . 8vo, 
Raphael, F. C. Localization of Faults in Electric Light and Power Mains. 

8vo, 

Rathbone, R. L. B. Simple Jewellery 8vo, 

Rateau, A. Flow of Steam through Nozzles and Orifices. Trans, by H. 

B. Brydon 8vo, 

Rausenberger, F. The Theory of the Recoil of Guns 8vo, 

Rautenstrauch, W. Notes on the Elements of Machine Design, 8vo, boards, 
Rautenstrauch, W., and Williams, J. T. Machine Drafting and Empirical 

Design. 

Part I. Machine Drafting 8vo, *i 25 

Part II. Empirical Design (hi Preparation.) 

Raymond, E. B. Alternating Current Engineering i2mo, 

Rayner, H. Silk Throwing and Waste Silk Spinning 8vo, 

Recipes for the Color, Paint, Varnish, Oil, Soap and Drysaltery Trades . 8vo, 

Recipes for Flint Glass Making i2mo, 

Redwood, B. Petroleum. (Science Series No. 92.) i6mo, 

Reed's Engineers' Handbook 8vo, 

Key to the Nineteenth Edition of Reed's Engineers' Handbook . . 8vo, 

Useful Hints to Sea-going Engineers. nmo, 

Marine Boilers i2mo, 

Reinhardt, C. W. Lettering for Draftsmen, Engineers, and Students. 

oblong 4to, boards, 

The Technic of Mechanical Drafting oblong 4to, boards, 

Reiser, F. Hardening and Tempering of Steel. Trans, by A. Morris and 

H. Robson nrao, *2 50 

Reiser, N. Faults in the Manufacture of Woolen Goods. Trans, by A. 

Morris and H. Robson 8vo, *2 50 

Spinning and Weaving Calculations 8vo, *5 00 

Renwick, W. G. Marble and Marble Working 8vo, 5 00 

Reynolds, 0., and Idell, F. E. Triple Expansion Engines. (Science 

Series No. 99.) i6mo, o 50 






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20 D VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Rhead, G. F. Simple Structural Woodwork i2mo, *i oo 

Rice, J. M., and Johnson, W- W. A New Method of Obtaining the Differ- 
ential of Functions nmo, o 50 

Richardson, Jo The Modern Steam Engine 8vo, *3 50 

Richardson, S. S. Magnetism and Electricity i2mo, *2 00 

Rideal, S. Glue and Glue Testing. 8vo, *4 00 

Rings, F. Concrete in Theory and Practice i2mo, *2 50 

Ripper, W. Course of Instruction in Machine Drawing folio, *6 00 

Roberts, F. C. Figure of the Earth. (Science Series No. 79.) i6mo, o 50 

Roberts, J., Jr. Laboratory Work in Electrical Engineering 8vo, *2 00 

Robertson, L. S. Water-tube Boilers 8vo, 3 00 

Robinson, J. B. Architectural Composition 8vo, *2 50 

Robinson, S. W, Practical Treatise on the Teeth of Wheels. (Science 

Series No. 24.) i6mo, o 50 

Railroad Economics. (Science Series No. 59.) i6mo, o 50 

Wrought Iron Bridge Members. (Science Series No. 60.) i6mo, o 50 

Roebling, J. A. Long and Short Span Railway Bridges folio, 25 00 

Rogers, A. A Laboratory Guide of Industrial Chemistry i2mo, *i 50 

Rogers, A., and Aubert, A. B. Industrial Chemistry (In Press.) 

Rogers, F. Magnetism of Iron Vessels. (Science Series No. 30.) . . i6mo, o 50 

Rollins, W. Notes on X-Light 8vo, *7 50 

Rose, J. The Pattern-makers' Assistant 8vo, 2 50 

Key to Engines and Engine-running i2mo, 2 50 

Rose, T. K. The Precious Metals. (Westminster Series.) 8vo, *2 00 

Rosenhain, W. Glass Manufacture. (Westminster Series.) 8vo, *2 00 

Ross, W. A. Plowpipe in Chemistry and Metallurgy nmo, *2 00 

Rossiter, J. T. Steam Engines. (Westminster Series.). . .8vo (In Press.) 

Pumps and Pumping Machinery. (Westminster Series.).. 8vo (In Press.) 

Roth. Physical Chemistry 8vo, *2 00 

Rouillion, L. The Economics of Manual Training 8vo, 2 00 

Rowan, F. J. Practical Physics of the Modern Steam-boiler 8vo, 7 50 

Rowan, F. J., and Idell, F. E. Boiler Incrustation and Corrosion. 

(Science Series No. 27.) . i6mo, o 50 

Roxburgh, Wo General Foundry Practice 8vo, *3 50 

Ruhmer, E. Wireless Telephony. Trans, by J. Erskine-Murray .... 8vo, *3 50 

Russell, A. Theory of Electric Cables and Networks 8vo, *3 00 

Sabine, R. History and Progress of the Electric Telegraph i2mo, 1 25 

Saeltzer, A. Treatise on Acoustics i2mo, 1 00 

Salomons, D. Electric Light Installations. i2mo. 

Vol. I. The Management of Accumulators 2 50 

Vol. II. Apparatus 2 25 

Vol. III. Applications 1 50 

Sanford, P. G. Nitro-explosives 8vo, *4 00 

Saunders, C. H. Handbook of Practical Mechanics i6mo, 1 00 

leather, 1 25 

Saunnier, C. Watchmaker's Handbook i2mo, 3 00 

Sayers, H. M. Brakes for Tram Cars 8vo, *i 25 

Scheele, C. W. Chemical Essays , 8vo, *2 00 

Schellen, H. Magneto-electric and Dynamo-electric Machines 8vo, 5 00 

Scherer, R. Casein. Trans, by C. Salter 8vo, *3 00 



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D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG- 21 

Schmall, C. N. First Course in Analytic Geometry, Plane and Solid. 

i2mo, half leather, 
Schmall, C. N., and Shack, S. M. Elements of Plane Geometry. . . . nmo, 

Schmeer, L. Flow of Water 8vo, 

Schumann, F. A Manual of Heating and Ventilation i2mo, leather, 

Schwarz, E. H. L. Causal Geology 8vo, 

Schweizer, V., Distillation of Resins 8vo, 

Scott, W. W. Qualitative Analysis. A Laboratory Manual 8vo, 

Scribner, J. M. -Engineers' and Mechanics' Companion . . . i6mo, leather, 
Searle, G. M. " Sumners' Method." Condensed and Improved. (Science 

Series No. 124.) i6mo, 

Seaton, A. E. Manual of Marine Engineering 8vo, 

Seaton, A. E., and Rounthwaite, H. M. Pocket-book of Marine Engineer- 
ing i6mo, leather, 3 00 

Seeligmann, T., Torrilhon, G. L., and Falconnet, H. India Rubber and 

Gutta Percha. Trans, by J. G. Mcintosh 8vo, 

Seidell, A. Solubilities of Inorganic and Organic Substances 8vo, 

Sellew, W. H. Steel Rails 4to (In Press.) 

Senter, G. Outlines of Physical Chemistry nmo, 

Sever, G. F. Electric Engineering Experiments 8vo, boards, 

Sever, G. F., and Townsend, F. Laboratory and Factory Tests in Electrical 

Engineering 8vo, 

Sewall, C. H. Wireless Telegraphy 8vo, 

Lessons in Telegraphy nmo, 

Sewell, T. Elements of Electrical Engineering 8vo, 

The Construction of Dynamos 8vo, 

Sexton, A. H. Fuel and Refractory Materials i2mo, 

Chemistry of the Materials of Engineering i2mo, 

Alloys (Non- Ferrous) 8vo, 

The Metallurgy of Iron and Steel 8vo, 

Seymour, A. Practical Lithography 8vo, 

Modern Printing Inks 8vo, 

Shaw, Henry S. H. Mechanical Integrators. (Science Series No. 83.) 

i6mo, 

Shaw, P. E. Course of Practical Magnetism and Electricity 8vo, 

Shaw, S. History of the Staffordshire Potteries 8vo, 

Chemistry of Compounds Used in Porcelain Manufacture 8vo, 

Sheldon, S., and Hausmann, E. Direct Current Machines 8vo, 

Sheldon, S., Mason, H., and Hausmann, E. Alternating-current Machines. 

8vo, 

Sherer, R. Casein. Trans, by C. Salter 8vo, 

Sherriff, F. F. Oil Merchants' Manual i2mo, 

Shields, J. E. Notes on Engineering Construction i2mo, 

Shock, W. H. Steam Boilers 4to, half morocco, 

Shreve, S. H. Strength of Bridges and Roofs 8vo, 

Shunk, W. F. The Field Engineer i2mo, morocco, 

Simmons, W. H., and Appleton, H. A. Handbook of Soap Manufacture. 

8vo, 

Simms, F. W. The Principles and Practice of Leveling 8vo, 

Practical Tunneling 8vo, 

Simpson, G. The Naval Constructor i2mo, morocco, 



+ 5 


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22 D. VAN NOSTRAND COMPANY'S SHORT TITLE CATALOG 

Sinclair, A. Development of the Locomotive Engine . . . 8vo, half leather, 
Sindall, R. W. Manufacture of Paper. (Westminster Series.) ...... .8vo, 

Sloane, T. O'C. Elementary Electrical Calculations i2mo, 

Smith, C. F. Practical Alternating Currents and Testing 8vo, 

Practical Testing of Dynamos and Motors. 8vo, 

Smith, F. E. Handbook of General Instruction for Mechanics . . . nmo, 
Smith, I. W. The Theory of Deflections and of Latitudes and Departures. 

i6mo, morocco, 

Smith, J. C. Manufacture of Paint 8vo, 

Smith, W. Chemistry of Hat Manufacturing i2mo, 

Snell, A. T. Electric Motive Power 8vo, 

Snow, W. G. Pocketbook of Steam Heating and Ventilation. (In Press.) 
Snow, W. G., and Nolan, T. Ventilation of Buildings. (Science Series 

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WrOWVMWt 



ELECTRICAL 

t^mmmam Completely Reviled aHMMi 

ENGINEERS 

MMMHHM and Enlarged aMMMaHl 

POCKET BOOK 



1600 pp. 1128 in. 718 Table* i 



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